• 5^(3i)

    From Richard Hachel@21:1/5 to All on Sat Jul 12 10:28:26 2025
    XPost: fr.sci.maths

    La question du jour est donc : combien font 5^(3i)?

    Si l'on demande à un mathématicien combien font 2*2, le mathématicien
    saura répondre.

    2*2 font 4.

    Si on lui demande combien font 9*4, hormis Python, notre sympathique utilisateur Nemo, mais qui semble avoir de très gros problème avec l'arithmétique, le mathématicien répondra que cela fait 36 (et pas sept virgule deux comme le suggère notre ami sur fr.sci.physique).

    Pourquoi ces bonnes réponses universelles?

    Parce que les mathématiciens ne sont pas des cancres. Même à l'école primaire, on sait que 2*2 font 4, et que 9 fois 4 font 36.

    Mais, de même qu'en relativité restreinte où Albert Einstein et Hermann Minkowski ont fait dévier le courant de la pensée de Poincaré plus
    qu'ils ne l'on porté un centimètre plus loin, un problème va se poser
    dès que les mathématiciens vont considérer l'entité imaginaire i.

    Et de même que l'immense docteur Hachel (c'est moi), surnommé le
    luminaire céleste de usenet, a révolutionné les notions relativistes de façon foudroyante, on peut, peut-être, se poser des questions sur le
    concept imaginaire et tenter des réponses là où il semblerait qu'il n'y
    en a pas.

    Qu'est ce que i? Ce n'est pas un nombre, et on peut s'étonner que les mathématiciens voient là un nombre.

    C'est un opérateur. Comme la racine carrée, ou le logarithme.

    Ainsi, par exemple, 1(opérateur i)=-1.

    Ou 1(i²)=-1 comme c'est bien connu. De là, c'est facile : i^x=-1 quelque
    soit x, et (-i)^x = +1 ou -1 selon la parité de x. (-i)^3=1. (-i)^4=-1.

    Cela est trivial ; alors il faut aller plus loin.

    Et en exposant? Que devient i? Quel opérateur devient-il?

    Posons y=5^(3i)

    Combien cela fait-il? Il semblerait qu'aucun mathématicien ne sache
    répondre sur cette question de lycée.

    Je vais tenter une réponse, merci de bien suivre l'exposé.

    y=5^(3i) est un point sur l'échelle y de la courbe y=5^x où x=3i.

    Traçons y=5^x. Facile. Une simple exponentielle passant pas $(0,1) puis
    par (1,5), (2,25), etc...

    Mais où se trouve 3i sur x?

    Le bon docteur Hachel, nous a montré, de façon très élégante, que 3i
    se trouvait en position (-3,0) sur une représentation cartésienne (il
    n'est pas besoin de parler de représentation de Gauss-Argand, nous
    étudions les imaginaires purs, pas les complexes, dont l'utilité est
    ailleurs ; comme en électromagnétisme ou en électricité).

    Il suffit donc de retrouver le y attenant à la contre-courbe imaginaire
    g(x) en symétrie de point $(0,y₀).

    g(x), qu'est-ce?

    C'est g(x)=-f(-x)+y₀, soit ici, g(x)=-5^(-x)+2

    On voit que si x=-1, par exemple g(x)=-5+2=-3, et donc que si x=i alors f(x)=-3. Bref 5^i=-3

    Cherchons 5^(3i). On a par symétrie de point $, 5^3=125 comme chacun
    sait.

    Soit : il existe un point f(x)=(3,125) pour f(x)=5^x et donc un point g(x)--$-->(-3,-123).

    Ce qui nous donne 5^(3i)=-123

    C'est un peu contre-intuitif d'avoir un résultat négatif mais il ne faut
    pas oublier que ^i est un agent de rotation de 180° de la courbe en la
    partie haute de droite, devient basse de gauche, et passer de (3,125) à (-3,-123) puisqu'il ne faut pas oublier de retrancher 2y₀, et ici
    y₀=1.


    Je vous remercie de votre attention.

    R.H.

    --- SoupGate-Win32 v1.05
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  • From sobriquet@21:1/5 to All on Sat Jul 12 23:03:47 2025
    Op 12/07/2025 om 12:28 schreef Richard Hachel:
    [...]

    Wolfram Alpha says 5^(3i) = cos(3*ln(5))+i*sin(3*ln(5)), so it seems you
    still haven't figured out what complex numbers are or how they work.

    Not just Wolfram Alpha, any graphic calculator that is able to handle
    complex numbers.

    https://www.desmos.com/calculator/f3ovmqpg3x

    There is not a single online source that will confirm or support your
    claim that 5^(3i) = (-3,-123).

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Hachel@21:1/5 to All on Sat Jul 12 22:18:12 2025
    Le 12/07/2025 à 23:03, sobriquet a écrit :
    Op 12/07/2025 om 12:28 schreef Richard Hachel:
    [...]

    Wolfram Alpha says 5^(3i) = cos(3*ln(5))+i*sin(3*ln(5)), so it seems you still haven't figured out what complex numbers are or how they work.

    Not just Wolfram Alpha, any graphic calculator that is able to handle
    complex numbers.

    https://www.desmos.com/calculator/f3ovmqpg3x

    There is not a single online source that will confirm or support your
    claim that 5^(3i) = (-3,-123).

    That's not quite what I said, the value x=5^(3i) is not a point, but a
    value.
    x=-123

    R.H.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Python@21:1/5 to All on Sat Jul 12 22:20:28 2025
    XPost: fr.sci.maths

    Le 12/07/2025 à 23:55, Richard Hachel a écrit :
    Le 12/07/2025 à 23:01, sobriquet a écrit :
    Op 12/07/2025 om 12:28 schreef Richard Hachel:
    [...]

    Wolfram Alpha says 5^(3i) = cos(3*ln(5))+i*sin(3*ln(5)), so it seems you
    still haven't figured out what complex numbers are or how they work.

    Not just Wolfram Alpha, any graphic calculator that is able to handle
    complex numbers.

    https://www.desmos.com/calculator/f3ovmqpg3x

    There is not a single online source that will confirm or support your
    claim that 5^(3i) = (-3,-123).

    That's not quite what I said, the value x=5^(3i) is not a point, but a value. x=-123

    R.H.

    Still wrong and nonsense though.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Sun Jul 13 00:35:58 2025
    Op 13/07/2025 om 00:18 schreef Richard Hachel:
    Le 12/07/2025 à 23:03, sobriquet a écrit :
    Op 12/07/2025 om 12:28 schreef Richard Hachel:
    ;[...]

    Wolfram Alpha says 5^(3i) = cos(3*ln(5))+i*sin(3*ln(5)), so it seems
    you still haven't figured out what complex numbers are or how they work.

    Not just Wolfram Alpha, any graphic calculator that is able to handle
    complex numbers.

    https://www.desmos.com/calculator/f3ovmqpg3x

    There is not a single online source that will confirm or support your
    claim that 5^(3i) = (-3,-123).

    That's not quite what I said, the value x=5^(3i) is not a point, but a
    value.
    x=-123

    R.H.

    You're right, my mistake. But still, 5^(3i) is not equal to -123 and you
    can't point to any online source that will substantiate that claim.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From WM@21:1/5 to sobriquet on Sun Jul 13 14:08:36 2025
    On 13.07.2025 00:35, sobriquet wrote:
    Op 13/07/2025 om 00:18 schreef Richard Hachel:
    Le 12/07/2025 à 23:03, sobriquet a écrit :
    Op 12/07/2025 om 12:28 schreef Richard Hachel:
    ;[...]

    Wolfram Alpha says 5^(3i) = cos(3*ln(5))+i*sin(3*ln(5)), so it seems
    you still haven't figured out what complex numbers are or how they work. >>>
    Not just Wolfram Alpha, any graphic calculator that is able to handle
    complex numbers.

    https://www.desmos.com/calculator/f3ovmqpg3x

    There is not a single online source that will confirm or support your
    claim that 5^(3i) = (-3,-123).

    That's not quite what I said, the value x=5^(3i) is not a point, but a
    value.
    x=-123

    You're right, my mistake.
    What mistake? Dropping the 2kπ we get without Wolfram
    5^(3i) = e^ln(5^(3i)) = (e^(3i*ln5) = cos(3*ln5) + i*sin(3*ln5)

    Regards, WM

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Hachel@21:1/5 to All on Sun Jul 13 13:06:00 2025
    Le 13/07/2025 à 14:08, WM a écrit :
    On 13.07.2025 00:35, sobriquet wrote:
    Op 13/07/2025 om 00:18 schreef Richard Hachel:
    Le 12/07/2025 à 23:03, sobriquet a écrit :
    Op 12/07/2025 om 12:28 schreef Richard Hachel:
    ;[...]

    Wolfram Alpha says 5^(3i) = cos(3*ln(5))+i*sin(3*ln(5)), so it seems
    you still haven't figured out what complex numbers are or how they work. >>>>
    Not just Wolfram Alpha, any graphic calculator that is able to handle
    complex numbers.

    https://www.desmos.com/calculator/f3ovmqpg3x

    There is not a single online source that will confirm or support your
    claim that 5^(3i) = (-3,-123).

    That's not quite what I said, the value x=5^(3i) is not a point, but a
    value.
    x=-123

    You're right, my mistake.
    What mistake? Dropping the 2kπ we get without Wolfram
    5^(3i) = e^ln(5^(3i)) = (e^(3i*ln5) = cos(3*ln5) + i*sin(3*ln5)

    Regards, WM

    Log5=1.609437912

    Log5*3=4.828313737

    Wath is cos(4.828313737) ?

    R.H.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Sun Jul 13 14:21:17 2025
    Op 13/07/2025 om 14:08 schreef WM:
    On 13.07.2025 00:35, sobriquet wrote:
    Op 13/07/2025 om 00:18 schreef Richard Hachel:
    Le 12/07/2025 à 23:03, sobriquet a écrit :
    Op 12/07/2025 om 12:28 schreef Richard Hachel:
    ;[...]

    Wolfram Alpha says 5^(3i) = cos(3*ln(5))+i*sin(3*ln(5)), so it seems
    you still haven't figured out what complex numbers are or how they
    work.

    Not just Wolfram Alpha, any graphic calculator that is able to
    handle complex numbers.

    https://www.desmos.com/calculator/f3ovmqpg3x

    There is not a single online source that will confirm or support
    your claim that 5^(3i) = (-3,-123).

    That's not quite what I said, the value x=5^(3i) is not a point, but
    a value.
    x=-123

    You're right, my mistake.
    What mistake? Dropping the 2kπ we get without Wolfram
    5^(3i) = e^ln(5^(3i)) = (e^(3i*ln5) = cos(3*ln5) + i*sin(3*ln5)

    Regards, WM


    My mistake of saying Richard Hachel said that 5^(3i) = (-3,-123) while
    he actually said that 5^(3i) = -123

    I agree that 5^(3i) = cos(3*ln(5)) + i*sin(3*ln(5))

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Hachel@21:1/5 to All on Sun Jul 13 13:11:21 2025
    Le 13/07/2025 à 14:21, sobriquet a écrit :
    Op 13/07/2025 om 14:08 schreef WM:
    On 13.07.2025 00:35, sobriquet wrote:
    Op 13/07/2025 om 00:18 schreef Richard Hachel:
    Le 12/07/2025 à 23:03, sobriquet a écrit :
    Op 12/07/2025 om 12:28 schreef Richard Hachel:
    ;[...]

    Wolfram Alpha says 5^(3i) = cos(3*ln(5))+i*sin(3*ln(5)), so it seems >>>>> you still haven't figured out what complex numbers are or how they
    work.

    Not just Wolfram Alpha, any graphic calculator that is able to
    handle complex numbers.

    https://www.desmos.com/calculator/f3ovmqpg3x

    There is not a single online source that will confirm or support
    your claim that 5^(3i) = (-3,-123).

    That's not quite what I said, the value x=5^(3i) is not a point, but
    a value.
    x=-123

    You're right, my mistake.
    What mistake? Dropping the 2kπ we get without Wolfram
    5^(3i) = e^ln(5^(3i)) = (e^(3i*ln5) = cos(3*ln5) + i*sin(3*ln5)

    Regards, WM


    My mistake of saying Richard Hachel said that 5^(3i) = (-3,-123) while
    he actually said that 5^(3i) = -123

    I agree that 5^(3i) = cos(3*ln(5)) + i*sin(3*ln(5))

    I agree that, in algebric analysis, 5^(3i) = -123

    In complex geometria, I can't understand what term y=5^(3i) is. A round
    square?

    R.H.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From WM@21:1/5 to Richard Hachel on Sun Jul 13 15:58:51 2025
    On 13.07.2025 15:06, Richard Hachel wrote:
    Le 13/07/2025 à 14:08, WM a écrit :
    On 13.07.2025 00:35, sobriquet wrote:
    Op 13/07/2025 om 00:18 schreef Richard Hachel:
    Le 12/07/2025 à 23:03, sobriquet a écrit :
    Op 12/07/2025 om 12:28 schreef Richard Hachel:
    ;[...]

    Wolfram Alpha says 5^(3i) = cos(3*ln(5))+i*sin(3*ln(5)), so it
    seems you still haven't figured out what complex numbers are or how
    they work.

    Not just Wolfram Alpha, any graphic calculator that is able to
    handle complex numbers.

    https://www.desmos.com/calculator/f3ovmqpg3x

    There is not a single online source that will confirm or support
    your claim that 5^(3i) = (-3,-123).

    That's not quite what I said, the value x=5^(3i) is not a point, but
    a value.
    x=-123

    You're right, my mistake.
    What mistake? Dropping the 2kπ we get without Wolfram
    5^(3i) = e^ln(5^(3i)) = (e^(3i*ln5) = cos(3*ln5) + i*sin(3*ln5)

    Log5=1.609437912

    Log5*3=4.828313737

    Wath is cos(4.828313737) ?

    = 0.115...

    Regards, WM

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Sun Jul 13 19:23:57 2025
    Op 13/07/2025 om 15:11 schreef Richard Hachel:
    Le 13/07/2025 à 14:21, sobriquet a écrit :
    Op 13/07/2025 om 14:08 schreef WM:
    On 13.07.2025 00:35, sobriquet wrote:
    Op 13/07/2025 om 00:18 schreef Richard Hachel:
    Le 12/07/2025 à 23:03, sobriquet a écrit :
    Op 12/07/2025 om 12:28 schreef Richard Hachel:
    ;[...]

    Wolfram Alpha says 5^(3i) = cos(3*ln(5))+i*sin(3*ln(5)), so it
    seems you still haven't figured out what complex numbers are or
    how they work.

    Not just Wolfram Alpha, any graphic calculator that is able to
    handle complex numbers.

    https://www.desmos.com/calculator/f3ovmqpg3x

    There is not a single online source that will confirm or support
    your claim that 5^(3i) = (-3,-123).

    That's not quite what I said, the value x=5^(3i) is not a point,
    but a value.
    x=-123

    You're right, my mistake.
    What mistake? Dropping the 2kπ we get without Wolfram
    5^(3i) = e^ln(5^(3i)) = (e^(3i*ln5) = cos(3*ln5) + i*sin(3*ln5)

    Regards, WM


    My mistake of saying Richard Hachel said that 5^(3i) = (-3,-123) while
    he actually said that 5^(3i) = -123

    I agree that 5^(3i) = cos(3*ln(5)) + i*sin(3*ln(5))

    I agree that, in algebric analysis,  5^(3i) = -123

    In complex geometria, I can't understand what term y=5^(3i) is. A round square?
    R.H.

    I think in a way you're right. Math is a confusing hodgepodge of ideas.
    It's basically full of shit. But there is hope that AI will debug all
    the math and make it logical and comprehensible.
    There are countless examples of math that historically makes sense, but
    tends to confuse people. Like mixed numbers.

    3 1/3 usually means 3 + 1/3

    But 3 e/pi means 3 * e/pi

    So a space is sometimes interpreted as addition and sometimes it's
    interpreted as multiplication.

    Math is full of idiotic nonsense like that, so it's really no wonder
    people can't make much sense of math.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From efji@21:1/5 to All on Sun Jul 13 19:49:52 2025
    Le 13/07/2025 à 19:23, sobriquet a écrit :


    3 1/3 usually means 3 + 1/3

    No. Never. 3 1/3 is a British/Yankee notation for groceries, nothing
    close to mathematics.

    Math is full of idiotic nonsense like that, so it's really no wonder
    people can't make much sense of math.

    Not at all. Mathematical notations are universal, precise and univoque.

    --
    F.J.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Python@21:1/5 to All on Sun Jul 13 17:30:41 2025
    Le 13/07/2025 à 19:23, sobriquet a écrit :
    Op 13/07/2025 om 15:11 schreef Richard Hachel:
    Le 13/07/2025 à 14:21, sobriquet a écrit :
    Op 13/07/2025 om 14:08 schreef WM:
    On 13.07.2025 00:35, sobriquet wrote:
    Op 13/07/2025 om 00:18 schreef Richard Hachel:
    Le 12/07/2025 à 23:03, sobriquet a écrit :
    Op 12/07/2025 om 12:28 schreef Richard Hachel:
    ;[...]

    Wolfram Alpha says 5^(3i) = cos(3*ln(5))+i*sin(3*ln(5)), so it
    seems you still haven't figured out what complex numbers are or
    how they work.

    Not just Wolfram Alpha, any graphic calculator that is able to
    handle complex numbers.

    https://www.desmos.com/calculator/f3ovmqpg3x

    There is not a single online source that will confirm or support >>>>>>> your claim that 5^(3i) = (-3,-123).

    That's not quite what I said, the value x=5^(3i) is not a point,
    but a value.
    x=-123

    You're right, my mistake.
    What mistake? Dropping the 2kπ we get without Wolfram
    5^(3i) = e^ln(5^(3i)) = (e^(3i*ln5) = cos(3*ln5) + i*sin(3*ln5)

    Regards, WM


    My mistake of saying Richard Hachel said that 5^(3i) = (-3,-123) while
    he actually said that 5^(3i) = -123

    I agree that 5^(3i) = cos(3*ln(5)) + i*sin(3*ln(5))

    I agree that, in algebric analysis,  5^(3i) = -123

    In complex geometria, I can't understand what term y=5^(3i) is. A round
    square?
    R.H.

    I think in a way you're right. Math is a confusing hodgepodge of ideas.
    It's basically full of shit. But there is hope that AI will debug all
    the math and make it logical and comprehensible.
    There are countless examples of math that historically makes sense, but
    tends to confuse people. Like mixed numbers.

    Ok, so you are a kind of "Hachel"-level crank. Didn't know that.

    3 1/3 usually means 3 + 1/3

    Definitely not. Where have you seen such habit?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Sun Jul 13 19:59:37 2025
    Op 13/07/2025 om 19:30 schreef Python:
    Le 13/07/2025 à 19:23, sobriquet a écrit :
    Op 13/07/2025 om 15:11 schreef Richard Hachel:
    Le 13/07/2025 à 14:21, sobriquet a écrit :
    Op 13/07/2025 om 14:08 schreef WM:
    On 13.07.2025 00:35, sobriquet wrote:
    Op 13/07/2025 om 00:18 schreef Richard Hachel:
    Le 12/07/2025 à 23:03, sobriquet a écrit :
    Op 12/07/2025 om 12:28 schreef Richard Hachel:
    ;[...]

    Wolfram Alpha says 5^(3i) = cos(3*ln(5))+i*sin(3*ln(5)), so it >>>>>>>> seems you still haven't figured out what complex numbers are or >>>>>>>> how they work.

    Not just Wolfram Alpha, any graphic calculator that is able to >>>>>>>> handle complex numbers.

    https://www.desmos.com/calculator/f3ovmqpg3x

    There is not a single online source that will confirm or support >>>>>>>> your claim that 5^(3i) = (-3,-123).

    That's not quite what I said, the value x=5^(3i) is not a point, >>>>>>> but a value.
    x=-123

    You're right, my mistake.
    What mistake? Dropping the 2kπ we get without Wolfram
    5^(3i) = e^ln(5^(3i)) = (e^(3i*ln5) = cos(3*ln5) + i*sin(3*ln5)

    Regards, WM


    My mistake of saying Richard Hachel said that 5^(3i) = (-3,-123)
    while he actually said that 5^(3i) = -123

    I agree that 5^(3i) = cos(3*ln(5)) + i*sin(3*ln(5))

    I agree that, in algebric analysis,  5^(3i) = -123

    In complex geometria, I can't understand what term y=5^(3i) is. A
    round square?
    R.H.

    I think in a way you're right. Math is a confusing hodgepodge of
    ideas. It's basically full of shit. But there is hope that AI will
    debug all the math and make it logical and comprehensible.
    There are countless examples of math that historically makes sense,
    but tends to confuse people. Like mixed numbers.

    Ok, so you are a kind of "Hachel"-level crank. Didn't know that.
    3 1/3 usually means 3 + 1/3

    Definitely not. Where have you seen such habit?

    https://www.wolframalpha.com/input?i=3+1%2F3

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Sun Jul 13 20:06:08 2025
    Op 13/07/2025 om 19:49 schreef efji:
    Le 13/07/2025 à 19:23, sobriquet a écrit :


    3 1/3 usually means 3 + 1/3

    No. Never. 3 1/3 is a British/Yankee notation for groceries, nothing
    close to mathematics.

    Math is full of idiotic nonsense like that, so it's really no wonder
    people can't make much sense of math.

    Not at all. Mathematical notations are universal, precise and univoque.


    Wolfram Alpha says arctan(1,2) = 1.10714871779409050301...

    Desmos says arctan(1,2) = 0.463647609001...

    https://www.wolframalpha.com/input?i=arctan%281%2C2%29

    https://www.desmos.com/calculator/dyjkhncmsk


    Now of course I know that they simply are using different conventions, arctan(x,y) vs arctan(y,x), but it doesn't take many of such
    inconsistencies to cause confusion or errors. It just goes to show
    that there are examples of different conventions in math.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From efji@21:1/5 to All on Sun Jul 13 20:44:37 2025
    Le 13/07/2025 à 20:06, sobriquet a écrit :
    Op 13/07/2025 om 19:49 schreef efji:
    Le 13/07/2025 à 19:23, sobriquet a écrit :


    3 1/3 usually means 3 + 1/3

    No. Never. 3 1/3 is a British/Yankee notation for groceries, nothing
    close to mathematics.

    Math is full of idiotic nonsense like that, so it's really no wonder
    people can't make much sense of math.

    Not at all. Mathematical notations are universal, precise and univoque.


    Wolfram Alpha says arctan(1,2) = 1.10714871779409050301...

    Desmos says arctan(1,2) = 0.463647609001...

    https://www.wolframalpha.com/input?i=arctan%281%2C2%29

    https://www.desmos.com/calculator/dyjkhncmsk


    Now of course I know that they simply are using different conventions, arctan(x,y) vs arctan(y,x), but it doesn't take many of such
    inconsistencies to cause confusion or errors. It just goes to show
    that there are examples of different conventions in math.

    Nothing above is "maths". You are talking about commercial products and softwares. Mathematical notations in books and article are not
    ambiguous. And in maths, there is nothing close to arctan(x,y) used
    without a proper definition given before.


    --
    F.J.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Python@21:1/5 to All on Sun Jul 13 18:38:40 2025
    Le 13/07/2025 à 19:49, efji a écrit :
    Le 13/07/2025 à 19:23, sobriquet a écrit :


    3 1/3 usually means 3 + 1/3

    No. Never. 3 1/3 is a British/Yankee notation for groceries, nothing
    close to mathematics.

    Wolfram is accepting groceries notation? This is bad! IMHA it is a not a feature, it is a bug.

    Anyway Sobriquet is insincere here, acting as crank.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Sun Jul 13 20:47:43 2025
    Op 13/07/2025 om 20:38 schreef Python:
    Le 13/07/2025 à 19:49, efji a écrit :
    Le 13/07/2025 à 19:23, sobriquet a écrit :


    3 1/3 usually means 3 + 1/3

    No. Never. 3 1/3 is a British/Yankee notation for groceries, nothing
    close to mathematics.

    Wolfram is accepting groceries notation? This is bad! IMHA it is a not a feature, it is a bug.

    Anyway Sobriquet is insincere here, acting as crank.



    No. I love math and I would like it to be consistent. But I often see
    things that just don't make any sense at a conceptual level.
    Take for instance:

    sum n=0 to infinity x^(2n)/(2n)! = cosh(x)

    https://www.wolframalpha.com/input?i=sum+n%3D0+to+infinity+x%5E%282n%29%2F%282n%29%21

    You would think oh, that implies (if we take x=0):

    sum n=0 to infinity 0^(2n)/(2n)! = cosh(0)

    But wolfram says no:

    https://www.wolframalpha.com/input?i=sum+n%3D0+to+infinity+0%5E%282n%29%2F%282n%29%21

    If you say that 0^0 is 1, you can't say it is 1 sometimes and at other
    times it's not 1.. that is simply not a consistent way of dealing with
    the meaning of 0^0.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Python@21:1/5 to All on Sun Jul 13 18:49:59 2025
    Le 13/07/2025 à 20:47, sobriquet a écrit :
    Op 13/07/2025 om 20:38 schreef Python:
    Le 13/07/2025 à 19:49, efji a écrit :
    Le 13/07/2025 à 19:23, sobriquet a écrit :


    3 1/3 usually means 3 + 1/3

    No. Never. 3 1/3 is a British/Yankee notation for groceries, nothing
    close to mathematics.

    Wolfram is accepting groceries notation? This is bad! IMHA it is a not a
    feature, it is a bug.

    Anyway Sobriquet is insincere here, acting as crank.



    No. I love math and I would like it to be consistent. But I often see
    things that just don't make any sense at a conceptual level.
    Take for instance:

    sum n=0 to infinity x^(2n)/(2n)! = cosh(x)


    https://www.wolframalpha.com/input?i=sum+n%3D0+to+infinity+x%5E%282n%29%2F%282n%29%21

    You would think oh, that implies (if we take x=0):

    sum n=0 to infinity 0^(2n)/(2n)! = cosh(0)

    But wolfram says no:


    https://www.wolframalpha.com/input?i=sum+n%3D0+to+infinity+0%5E%282n%29%2F%282n%29%21

    If you say that 0^0 is 1, you can't say it is 1 sometimes and at other
    times it's not 1.. that is simply not a consistent way of dealing with
    the meaning of 0^0.

    Oh, come on... Not this old 0^0 stuff.

    Grow up.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Sun Jul 13 20:53:11 2025
    Op 13/07/2025 om 20:44 schreef efji:
    Le 13/07/2025 à 20:06, sobriquet a écrit :
    Op 13/07/2025 om 19:49 schreef efji:
    Le 13/07/2025 à 19:23, sobriquet a écrit :


    3 1/3 usually means 3 + 1/3

    No. Never. 3 1/3 is a British/Yankee notation for groceries, nothing
    close to mathematics.

    Math is full of idiotic nonsense like that, so it's really no wonder
    people can't make much sense of math.

    Not at all. Mathematical notations are universal, precise and univoque.


    Wolfram Alpha says arctan(1,2) = 1.10714871779409050301...

    Desmos says arctan(1,2) = 0.463647609001...

    https://www.wolframalpha.com/input?i=arctan%281%2C2%29

    https://www.desmos.com/calculator/dyjkhncmsk


    Now of course I know that they simply are using different conventions,
    arctan(x,y) vs arctan(y,x), but it doesn't take many of such
    inconsistencies to cause confusion or errors. It just goes to show
    that there are examples of different conventions in math.

    Nothing above is "maths". You are talking about commercial products and softwares. Mathematical notations in books and article are not
    ambiguous. And in maths, there is nothing close to arctan(x,y) used
    without a proper definition given before.



    Books and articles are commercial products just the same. It's just
    culture and there is no essential difference between software, books
    and articles.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Sun Jul 13 20:58:45 2025
    Op 13/07/2025 om 20:49 schreef Python:
    Le 13/07/2025 à 20:47, sobriquet a écrit :
    Op 13/07/2025 om 20:38 schreef Python:
    Le 13/07/2025 à 19:49, efji a écrit :
    Le 13/07/2025 à 19:23, sobriquet a écrit :


    3 1/3 usually means 3 + 1/3

    No. Never. 3 1/3 is a British/Yankee notation for groceries, nothing
    close to mathematics.

    Wolfram is accepting groceries notation? This is bad! IMHA it is a
    not a feature, it is a bug.

    Anyway Sobriquet is insincere here, acting as crank.



    No. I love math and I would like it to be consistent. But I often see
    things that just don't make any sense at a conceptual level.
    Take for instance:

    sum n=0 to infinity x^(2n)/(2n)! = cosh(x)


    https://www.wolframalpha.com/input?
    i=sum+n%3D0+to+infinity+x%5E%282n%29%2F%282n%29%21

    You would think oh, that implies (if we take x=0):

    sum n=0 to infinity 0^(2n)/(2n)! = cosh(0)

    But wolfram says no:


    https://www.wolframalpha.com/input?
    i=sum+n%3D0+to+infinity+0%5E%282n%29%2F%282n%29%21

    If you say that 0^0 is 1, you can't say it is 1 sometimes and at other
    times it's not 1.. that is simply not a consistent way of dealing with
    the meaning of 0^0.

    Oh, come on... Not this old 0^0 stuff.

    Grow up.


    So you claim math is perfectly consistent and if people point out clear inconsistencies in math, they are childish?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Python@21:1/5 to All on Sun Jul 13 19:48:31 2025
    Le 13/07/2025 à 20:58, sobriquet a écrit :
    Op 13/07/2025 om 20:49 schreef Python:
    Le 13/07/2025 à 20:47, sobriquet a écrit :
    Op 13/07/2025 om 20:38 schreef Python:
    Le 13/07/2025 à 19:49, efji a écrit :
    Le 13/07/2025 à 19:23, sobriquet a écrit :


    3 1/3 usually means 3 + 1/3

    No. Never. 3 1/3 is a British/Yankee notation for groceries, nothing >>>>> close to mathematics.

    Wolfram is accepting groceries notation? This is bad! IMHA it is a
    not a feature, it is a bug.

    Anyway Sobriquet is insincere here, acting as crank.



    No. I love math and I would like it to be consistent. But I often see
    things that just don't make any sense at a conceptual level.
    Take for instance:

    sum n=0 to infinity x^(2n)/(2n)! = cosh(x)


    https://www.wolframalpha.com/input?
    i=sum+n%3D0+to+infinity+x%5E%282n%29%2F%282n%29%21

    You would think oh, that implies (if we take x=0):

    sum n=0 to infinity 0^(2n)/(2n)! = cosh(0)

    But wolfram says no:


    https://www.wolframalpha.com/input?
    i=sum+n%3D0+to+infinity+0%5E%282n%29%2F%282n%29%21

    If you say that 0^0 is 1, you can't say it is 1 sometimes and at other
    times it's not 1.. that is simply not a consistent way of dealing with
    the meaning of 0^0.

    Oh, come on... Not this old 0^0 stuff.

    Grow up.


    So you claim math is perfectly consistent and if people point out clear inconsistencies in math, they are childish?

    NOTHING you pointed you never leaded to a mistake. People are clever
    enough to consider the context, are you?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From efji@21:1/5 to All on Sun Jul 13 22:08:09 2025
    Le 13/07/2025 à 20:58, sobriquet a écrit :


    So you claim math is perfectly consistent and if people point out clear inconsistencies in math, they are childish?


    Yes. At least in maths that you are able to understand.
    Childish or trolls.
    But you are welcome to point what you call "inconsistencies" :)

    --
    F.J.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Python@21:1/5 to All on Sun Jul 13 19:46:49 2025
    Le 13/07/2025 à 20:58, sobriquet a écrit :
    Op 13/07/2025 om 20:49 schreef Python:
    Le 13/07/2025 à 20:47, sobriquet a écrit :
    Op 13/07/2025 om 20:38 schreef Python:
    Le 13/07/2025 à 19:49, efji a écrit :
    Le 13/07/2025 à 19:23, sobriquet a écrit :


    3 1/3 usually means 3 + 1/3

    No. Never. 3 1/3 is a British/Yankee notation for groceries, nothing >>>>> close to mathematics.

    Wolfram is accepting groceries notation? This is bad! IMHA it is a
    not a feature, it is a bug.

    Anyway Sobriquet is insincere here, acting as crank.



    No. I love math and I would like it to be consistent. But I often see
    things that just don't make any sense at a conceptual level.
    Take for instance:

    sum n=0 to infinity x^(2n)/(2n)! = cosh(x)


    https://www.wolframalpha.com/input?
    i=sum+n%3D0+to+infinity+x%5E%282n%29%2F%282n%29%21

    You would think oh, that implies (if we take x=0):

    sum n=0 to infinity 0^(2n)/(2n)! = cosh(0)

    But wolfram says no:


    https://www.wolframalpha.com/input?
    i=sum+n%3D0+to+infinity+0%5E%282n%29%2F%282n%29%21

    If you say that 0^0 is 1, you can't say it is 1 sometimes and at other
    times it's not 1.. that is simply not a consistent way of dealing with
    the meaning of 0^0.

    Oh, come on... Not this old 0^0 stuff.

    Grow up.


    So you claim math is perfectly consistent and if people point out clear inconsistencies in math, they are childish?

    You're not talking about inconsistencies. You are pointing out somme
    sloppiness in notation that are harmless as everyone in the field,
    including students, notice and don't care. Over-correctness is sometime
    bad in any language btw.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Sun Jul 13 23:40:01 2025
    Op 13/07/2025 om 21:48 schreef Python:
    Le 13/07/2025 à 20:58, sobriquet a écrit :
    Op 13/07/2025 om 20:49 schreef Python:
    Le 13/07/2025 à 20:47, sobriquet a écrit :
    Op 13/07/2025 om 20:38 schreef Python:
    Le 13/07/2025 à 19:49, efji a écrit :
    Le 13/07/2025 à 19:23, sobriquet a écrit :


    3 1/3 usually means 3 + 1/3

    No. Never. 3 1/3 is a British/Yankee notation for groceries,
    nothing close to mathematics.

    Wolfram is accepting groceries notation? This is bad! IMHA it is a
    not a feature, it is a bug.

    Anyway Sobriquet is insincere here, acting as crank.



    No. I love math and I would like it to be consistent. But I often see
    things that just don't make any sense at a conceptual level.
    Take for instance:

    sum n=0 to infinity x^(2n)/(2n)! = cosh(x)


    https://www.wolframalpha.com/input?
    i=sum+n%3D0+to+infinity+x%5E%282n%29%2F%282n%29%21

    You would think oh, that implies (if we take x=0):

    sum n=0 to infinity 0^(2n)/(2n)! = cosh(0)

    But wolfram says no:


    https://www.wolframalpha.com/input?
    i=sum+n%3D0+to+infinity+0%5E%282n%29%2F%282n%29%21

    If you say that 0^0 is 1, you can't say it is 1 sometimes and at
    other times it's not 1.. that is simply not a consistent way of
    dealing with the meaning of 0^0.

    Oh, come on... Not this old 0^0 stuff.

    Grow up.


    So you claim math is perfectly consistent and if people point out
    clear inconsistencies in math, they are childish?

    NOTHING you pointed you never leaded to a mistake. People are clever
    enough to consider the context, are you?



    The whole point of math is that it is supposed to work regardless of the context. A calculator that usually tells you that 3+4=7 but will
    occasionally claim that 3+4=9 isn't very useful.

    Grok says:

    Yes, inconsistencies in conventions have led to catastrophic accidents.
    Here are two notable examples:

    Mars Climate Orbiter (1999): NASA's Mars Climate Orbiter disintegrated
    in Mars' atmosphere due to a unit conversion error. The spacecraft's
    navigation software used metric units (newtons), but the ground crew
    provided data in imperial units (pounds-force). This mismatch caused the orbiter to enter the atmosphere at an incorrect altitude, leading to its destruction. The loss was valued at approximately $125 million.
    Gimli Glider (1983): Air Canada Flight 143, a Boeing 767, ran out of
    fuel mid-flight due to a mix-up between metric and imperial units. The
    plane was one of the first in Canada to use metric measurements (liters
    and kilograms), but the ground crew calculated fuel in pounds. The
    aircraft was loaded with less than half the required fuel, forcing an
    emergency landing. Miraculously, the plane landed safely at an abandoned airstrip in Gimli, Manitoba, with no fatalities among the 69 people on
    board.
    These cases highlight how critical clear and consistent conventions are
    in high-stakes operations.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From efji@21:1/5 to All on Mon Jul 14 15:03:57 2025
    Le 14/07/2025 à 14:20, sobriquet a écrit :
    Op 13/07/2025 om 22:08 schreef efji:
    Le 13/07/2025 à 20:58, sobriquet a écrit :


    So you claim math is perfectly consistent and if people point out
    clear inconsistencies in math, they are childish?


    Yes. At least in maths that you are able to understand.
    Childish or trolls.
    But you are welcome to point what you call "inconsistencies" :)


    Ok, I clearly overstated my case by claiming that math is full of shit.
    But what I'm trying to get at is the feeling that math probably isn't
    always defined in the way that provides optimal conceptual clarity.

    Precise definition is one thing, independent of the "observer".
    Clarity is another thing. What is perfectly clear for me could be
    obscure for you :)

    Historically we can point to examples like Roman numerals, which were
    a kind of primitive number system that was clearly suboptimal in many respects compared to the later Hindu-Arabic number system.
    So in historical developments it is often the case that math evolves
    and ideas in math tend to shift where certain things that were generally assumed to be meaningless or nonsensical tend to get accepted later on,
    like negative numbers or complex numbers. Or things that seemed obvious
    on a conceptual level, like the shortest distance between two points
    being a straight line, that later became doubtful (in curved geometry).

    Yes, history of maths is chaotic. Concepts and notations have been fixed
    in a rigorous way only lately, in the late XIXth and in the XXth
    century. Have you heard about Bourbaki ?


    So ultimately we strive towards approximating a kind of ideal conceptual
    math framework where we'd like a minimal conceptual basis (no redundant concepts) that provides the most versatile and powerful conceptual toolbox. In that respect I'm interested in the psychology of crackpots that might claim that 1*1=2 or that 5^(3i)=-123.

    Don't spend to much time on them :)
    Actually it's a mystery to me...

    Is there a mathematical fact about such concepts, or is it just the
    majority opinion (whatever the math community claims must be right) or
    is it that we can potentially come up with a conceptual framework that underpins concepts like numbers or functions such that we can easily
    provide a rigorous argument of why one claim like 1*1=1 makes sense and another claim like 1*1=2 is nonsense.

    Yes. Everything called "theorem" is not questionable at all. It has been
    proven in a rigorous way, starting from a basic set of axioms and using inferences. What is crucial in every theorem is the set of hypothesis.
    For example, in an Euclidian space equipped with the Euclidian distance
    (the "classical" everyday distance), the straight line gives the
    shortest distance between 2 points, but you can imagine other spaces and
    other distances (a "distance" is an application that fulfills a precise
    set of properties) for which the straight line do not leads to the
    shortest path between 2 points. A "ball" can be a square for particular distances in 2d :)

    Or is it like relativity where one person can claim event A preceded
    event B and another person can claim event B preceded event A and they
    could both be right despite holding contradictory views, because they
    witness the events from different perspectives?

    Please don't :)
    Rel...ity is a bad keyword attracting the famous crank.


    With certain nonsense claims, like the sun revolving around the earth,
    it's easy to debunk it with evidence because we can empirically observe
    the solar system from a point in space where it's obvious that planets
    like the earth revolve around the sun. But with other nonsense claims

    It has been established way before the space conquest!

    about abstractions like numbers, sets or gods, it's not always so easy
    to categorically refute it. Like the claim that there exists a set that contains all sets or the claim that god can do anything.
    Can god create a stone that is so heavy that not even god can lift it?

    Sets or gods?
    What a strange comparison. Sets theory is perfectly clear !

    --
    F.J.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Mon Jul 14 14:20:13 2025
    Op 13/07/2025 om 22:08 schreef efji:
    Le 13/07/2025 à 20:58, sobriquet a écrit :


    So you claim math is perfectly consistent and if people point out
    clear inconsistencies in math, they are childish?


    Yes. At least in maths that you are able to understand.
    Childish or trolls.
    But you are welcome to point what you call "inconsistencies" :)


    Ok, I clearly overstated my case by claiming that math is full of shit.
    But what I'm trying to get at is the feeling that math probably isn't
    always defined in the way that provides optimal conceptual clarity. Historically we can point to examples like Roman numerals, which were
    a kind of primitive number system that was clearly suboptimal in many
    respects compared to the later Hindu-Arabic number system.
    So in historical developments it is often the case that math evolves
    and ideas in math tend to shift where certain things that were generally assumed to be meaningless or nonsensical tend to get accepted later on,
    like negative numbers or complex numbers. Or things that seemed obvious
    on a conceptual level, like the shortest distance between two points
    being a straight line, that later became doubtful (in curved geometry).

    So ultimately we strive towards approximating a kind of ideal conceptual
    math framework where we'd like a minimal conceptual basis (no redundant concepts) that provides the most versatile and powerful conceptual toolbox.
    In that respect I'm interested in the psychology of crackpots that might
    claim that 1*1=2 or that 5^(3i)=-123.
    Is there a mathematical fact about such concepts, or is it just the
    majority opinion (whatever the math community claims must be right) or
    is it that we can potentially come up with a conceptual framework that underpins concepts like numbers or functions such that we can easily
    provide a rigorous argument of why one claim like 1*1=1 makes sense and
    another claim like 1*1=2 is nonsense.
    Or is it like relativity where one person can claim event A preceded
    event B and another person can claim event B preceded event A and they
    could both be right despite holding contradictory views, because they
    witness the events from different perspectives?

    With certain nonsense claims, like the sun revolving around the earth,
    it's easy to debunk it with evidence because we can empirically observe
    the solar system from a point in space where it's obvious that planets
    like the earth revolve around the sun. But with other nonsense claims
    about abstractions like numbers, sets or gods, it's not always so easy
    to categorically refute it. Like the claim that there exists a set that contains all sets or the claim that god can do anything.
    Can god create a stone that is so heavy that not even god can lift it?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Hachel@21:1/5 to All on Mon Jul 14 18:11:55 2025
    Le 14/07/2025 à 14:20, sobriquet a écrit :
    Op 13/07/2025 om 22:08 schreef efji:

    In that respect I'm interested in the psychology of crackpots that might claim that 1*1=2 or that 5^(3i)=-123.

    In imaginary algebria (not in complex trigonomztria) :

    5^(3i)=-123

    y=5^(3i)

    f(y)=5^(x) with y₀=f(0)=1

    g(x)=-f(-x)+2y₀=-5^(-3i)+2

    y=-125+2=-123

    R.H.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Hachel@21:1/5 to All on Mon Jul 14 18:28:44 2025
    Le 14/07/2025 à 15:03, efji a écrit :
    Le 14/07/2025 à 14:20, sobriquet a écrit :

    In that respect I'm interested in the psychology of crackpots that might
    claim that 1*1=2 or that 5^(3i)=-123.

    Don't spend to much time on them :)
    Actually it's a mystery to me...

    Il y a effectivement un énorme mystère qui ne touche pas spécifiquement
    ce genre de "crackpot" ; mais qui touche je pense 99% de l'humanité,
    c'est à dire 99% de ceux qui les lisent.

    C'est beaucoup 99%.

    Ce que je vous supplie de comprendre, et supplierai encore de comprendre longtemps, c'est que 99% des humains ont un nombril. Celui qui ne comprend
    pas cela n'a rien compris de la psychologie humaine de base. Il est tout simplement idiot.

    Sur 100 professeurs de faculté, sur 100 étudiants dans une faculté, tu
    as 99% de petits nombrils. Ce sont tout simplement des hommes, parfois érudits, savants, mais des hommes.

    C'est ce qu'on pourrait appeler une sorte de péché originel.

    Lorsque Abel fait son offrande, le petit nombril de Caïn frémit.

    Toujours, toujours, le même problème se reproduit.

    Lorsque le docteur Hachel fait un petit scoop politique, donne une
    équation relativiste, explique un phénomène sociologique, propose une conversion mathématique, réfute une idéologie historique, explique l'ésotérique biblique, toujours, toujours, toujours le même phénomène
    se reproduit : "C'est un crank, ne l'écoutez pas".

    C'est systématique.

    Sauf que le mystère n'est pas en lui, mais en ceux qui le lisent.

    Qu'est ce qu'ils ont tous à voir du crank, du crank, encore du crank?

    Il faut donc tuer Hachel en révélant la vérité effroyable : c'est un
    crank, et il ne pense pas "comme nous".

    Caîn tue Abel (ici par le dénigrement).

    Toujours le même phénomène se reproduit comme une loi physique de gravitation.

    R.H.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Tristan Wibberley@21:1/5 to efji on Mon Jul 14 23:57:03 2025
    On 13/07/2025 19:44, efji wrote:
    Mathematical notations in books and article are not
    ambiguous.

    That's why I like two element column vectors of naturals so much.
    They're never written in the same way as a number of combinations or of permutations which, of course are always, in every school and tradition, written ⁿCᵣ and ⁿPᵣ respectively.

    BTW, even in one country, different high-schools teach different
    notations. Across countries and decades it's even more varied.

    And each student that doesn't talk with the other groups much thinks
    they've been taught correctly and the others need to start again with
    the one-true school.

    It's interesting to read Curry and Feys, Combinatory Logic 1, especially including all the supplementary notes where he discusses who's notation corresponds to who's and even more interesting to wonder about the
    definition of Strong Implication he references and see how he uses
    different notation across most of a decade as well as a different name
    in his U-language. Good evidence there is not one final notation.

    In my education from small child all the way until university, 3⅛ means
    3 + ⅛ yet 3x means 3 times x (perhaps ⅛ doesn't show up on your computer
    - it's 1/8 with small numbers). My maths education was pretty poor but
    you'll find it hard to find anyone in any town I've lived in that thinks
    3⅛ means anything but 3 + ⅛ unless they're trolling.

    I have a semi-famous book on real analysis from 1984 (its packed away so
    I can't check the author names) whose notation is self-ambiguous within
    the first defining chapters because of its disregard for sets containing
    sets and it doesn't bother to propose a sufficient structural
    restriction to resolve the ambiguity.

    --- SoupGate-Win32 v1.05
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  • From sobriquet@21:1/5 to All on Tue Jul 15 16:53:20 2025
    Op 14/07/2025 om 20:11 schreef Richard Hachel:
    Le 14/07/2025 à 14:20, sobriquet a écrit :
    Op 13/07/2025 om 22:08 schreef efji:

    In that respect I'm interested in the psychology of crackpots that might
    claim that 1*1=2 or that 5^(3i)=-123.

    In imaginary algebria (not in complex trigonomztria) :

    5^(3i)=-123

    y=5^(3i)

    f(y)=5^(x) with y₀=f(0)=1

    g(x)=-f(-x)+2y₀=-5^(-3i)+2

    y=-125+2=-123

    R.H.


    Yes, and what is 1/i in your crackpot approach?

    --- SoupGate-Win32 v1.05
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  • From sobriquet@21:1/5 to All on Tue Jul 15 17:13:58 2025
    Op 14/07/2025 om 15:03 schreef efji:
    Le 14/07/2025 à 14:20, sobriquet a écrit :
    Op 13/07/2025 om 22:08 schreef efji:
    Le 13/07/2025 à 20:58, sobriquet a écrit :


    So you claim math is perfectly consistent and if people point out
    clear inconsistencies in math, they are childish?


    Yes. At least in maths that you are able to understand.
    Childish or trolls.
    But you are welcome to point what you call "inconsistencies" :)


    Ok, I clearly overstated my case by claiming that math is full of shit.
    But what I'm trying to get at is the feeling that math probably isn't
    always defined in the way that provides optimal conceptual clarity.

    Precise definition is one thing, independent of the "observer".
    Clarity is another thing. What is perfectly clear for me could be
    obscure for you :)

    The goal of math is not to come up with the most unintelligible conceptualization. If we have a choice between two approaches that are
    equally useful and one of those approaches is much harder to understand
    or learn, it makes sense to pick the other approach that is more
    accessible for people who would like to learn it.


    Historically we can point to examples like Roman numerals, which were
    a kind of primitive number system that was clearly suboptimal in many
    respects compared to the later Hindu-Arabic number system.
    So in historical developments it is often the case that math evolves
    and ideas in math tend to shift where certain things that were
    generally assumed to be meaningless or nonsensical tend to get
    accepted later on, like negative numbers or complex numbers. Or things
    that seemed obvious on a conceptual level, like the shortest distance
    between two points being a straight line, that later became doubtful
    (in curved geometry).

    Yes, history of maths is chaotic. Concepts and notations have been fixed
    in a rigorous way only lately, in the late XIXth and in the XXth
    century. Have you heard about Bourbaki ?

    Yes. I think the Bourbaki group tended to dismiss intuition and visual approaches to math, like geometry, but I think it's often good to have a balance between symbolic/algebraic approaches and geometric approaches,
    so you get the best of both. Both approaches have pros and cons and they
    can mutually support and reinforce one another.

    [..]

    With certain nonsense claims, like the sun revolving around the earth,
    it's easy to debunk it with evidence because we can empirically
    observe the solar system from a point in space where it's obvious that
    planets like the earth revolve around the sun. But with other nonsense
    claims

    It has been established way before the space conquest!

    Sure, it's just a way to provide the most clear and intuitive empirical evidence for the claim that planets revolve around the sun.


    about abstractions like numbers, sets or gods, it's not always so easy
    to categorically refute it. Like the claim that there exists a set
    that contains all sets or the claim that god can do anything.
    Can god create a stone that is so heavy that not even god can lift it?

    Sets or gods?
    What a strange comparison. Sets theory is perfectly clear !

    They are both abstractions of things that exist in our mind while it's
    not entirely clear if they also exist in the real world somehow.
    Though gods are outside the realm of math, but in epistemological or ontological respect there are similar issues of how we're supposed to differentiate between fact and fiction in case of things that lack an unambiguous basis in the form of empirical evidence.

    --- SoupGate-Win32 v1.05
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  • From Richard Hachel@21:1/5 to All on Tue Jul 15 15:38:19 2025
    Le 15/07/2025 à 16:53, sobriquet a écrit :
    Op 14/07/2025 om 20:11 schreef Richard Hachel:
    Le 14/07/2025 à 14:20, sobriquet a écrit :
    Op 13/07/2025 om 22:08 schreef efji:

    In that respect I'm interested in the psychology of crackpots that might >>> claim that 1*1=2 or that 5^(3i)=-123.

    In imaginary algebria (not in complex trigonomztria) :

    5^(3i)=-123

    y=5^(3i)

    f(y)=5^(x) with y₀=f(0)=1

    g(x)=-f(-x)+2y₀=-5^(-3i)+2

    y=-125+2=-123

    R.H.


    Yes, and what is 1/i in your crackpot approach?

    Merci de bien vouloir respecter votre interlocuteur, ce mépris à la con devient intolérable.

    Je réponds quand même non pour vous, mais pour ceux que ça pourrait intéresser.

    Qu'avons nous dit? Que i n'était pas un nombre, mais un
    opérateur.

    Et que lorsqu'il était écrit sous forme simple i, il voulait dire
    i=1*i=-1.

    Puisque i^x=-1 quelque soit x, et que (-i)^x dépend de la parité de x.

    Ici, on pose la question : y=1/i.

    La réponse est d'une dramatique simplicité.

    1/i=i^(-1)

    Nous venons de dire que i^x=-1 quelque soit x.

    1/i=-1

    Attention au piège, certains rigolos se sentant malins pourrait dire que
    l'on va multiplier par i
    les deux termes du quotient, mais c'est une erreur de concept. On aurait
    alors i/i²=-1/-1=1
    SAUF QUE i est un opérateur, et qu'il ne sert à rien de le répéter
    deux fois. C'est pas comme ça que ça marche.

    R.H.

    --- SoupGate-Win32 v1.05
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  • From Python@21:1/5 to All on Tue Jul 15 17:01:57 2025
    Le 15/07/2025 à 17:38, Richard Hachel a écrit :
    Le 15/07/2025 à 16:53, sobriquet a écrit :
    Op 14/07/2025 om 20:11 schreef Richard Hachel:
    Le 14/07/2025 à 14:20, sobriquet a écrit :
    Op 13/07/2025 om 22:08 schreef efji:

    In that respect I'm interested in the psychology of crackpots that might >>>> claim that 1*1=2 or that 5^(3i)=-123.

    In imaginary algebria (not in complex trigonomztria) :

    5^(3i)=-123

    y=5^(3i)

    f(y)=5^(x) with y₀=f(0)=1

    g(x)=-f(-x)+2y₀=-5^(-3i)+2

    y=-125+2=-123

    R.H.


    Yes, and what is 1/i in your crackpot approach?

    Merci de bien vouloir respecter votre interlocuteur, ce mépris à la con devient intolérable.

    The qualification of crackpot is appropriate in your case.

    Posting in French in an English-speaking group IS a lack of respect.

    --- SoupGate-Win32 v1.05
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  • From Richard Hachel@21:1/5 to All on Tue Jul 15 17:53:43 2025
    Le 15/07/2025 à 19:01, Python a écrit :
    Le 15/07/2025 à 17:38, Richard Hachel a écrit :
    Le 15/07/2025 à 16:53, sobriquet a écrit :

    Posting in French in an English-speaking group IS a lack of respect.

    A lack of respect?

    Mais monsieur, vous n'oseriez pas!

    R.H.

    --- SoupGate-Win32 v1.05
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  • From WM@21:1/5 to efji on Tue Jul 15 21:28:11 2025
    On 14.07.2025 15:03, efji wrote:

    Sets theory is perfectly clear !

    and clearly wrong.

    Proofs:

    "Proof of the existence of dark numbers (bilingual version)",
    OSFPREPRINTS (Nov 2022)
    https://osf.io/preprints/osf/tyvnk_v1

    "New proof of dark numbers by means of the thinned out harmonic series", OSFPREPRINTS (10 Mar 2025)
    https://osf.io/preprints/osf/53qg2_v1?view_only=

    Regards, WM

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Tue Jul 15 22:17:38 2025
    Op 15/07/2025 om 17:38 schreef Richard Hachel:
    Le 15/07/2025 à 16:53, sobriquet a écrit :
    [...]
    Yes, and what is 1/i in your crackpot approach?

    Merci de bien vouloir respecter votre interlocuteur, ce mépris à la con devient intolérable.

    Je réponds quand même non pour vous, mais pour ceux que ça pourrait intéresser.

    Qu'avons nous dit? Que i n'était pas un nombre, mais un opérateur.
    Et que lorsqu'il était écrit sous forme simple i, il voulait dire i=1*i=-1.

    Puisque i^x=-1 quelque soit x, et que (-i)^x dépend de la parité de x.
    Ici, on pose la question : y=1/i.

    La réponse est d'une dramatique simplicité.

    1/i=i^(-1)

    Nous venons de dire que i^x=-1 quelque soit x.

    1/i=-1

    Attention au piège, certains rigolos se sentant malins pourrait dire que l'on va multiplier par i les deux termes du quotient, mais c'est une
    erreur de concept. On aurait alors i/i²=-1/-1=1 SAUF QUE i est un opérateur, et qu'il ne sert à rien de le répéter deux fois. C'est pas comme ça que ça marche.
    R.H.




    Ok, and what is tan(i + pi/2)?

    --- SoupGate-Win32 v1.05
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  • From Richard Hachel@21:1/5 to All on Tue Jul 15 21:06:05 2025
    Le 15/07/2025 à 22:17, sobriquet a écrit :
    Op 15/07/2025 om 17:38 schreef Richard Hachel:
    Le 15/07/2025 à 16:53, sobriquet a écrit :
    [...]
    Yes, and what is 1/i in your crackpot approach?

    Merci de bien vouloir respecter votre interlocuteur, ce mépris à la con
    devient intolérable.

    Je réponds quand même non pour vous, mais pour ceux que ça pourrait
    intéresser.

    Qu'avons nous dit? Que i n'était pas un nombre, mais un opérateur.
    Et que lorsqu'il était écrit sous forme simple i, il voulait dire i=1*i=-1.

    Puisque i^x=-1 quelque soit x, et que (-i)^x dépend de la parité de x.
    Ici, on pose la question : y=1/i.

    La réponse est d'une dramatique simplicité.

    1/i=i^(-1)

    Nous venons de dire que i^x=-1 quelque soit x.

    1/i=-1

    Attention au piège, certains rigolos se sentant malins pourrait dire que
    l'on va multiplier par i les deux termes du quotient, mais c'est une
    erreur de concept. On aurait alors i/i²=-1/-1=1 SAUF QUE i est un
    opérateur, et qu'il ne sert à rien de le répéter deux fois. C'est pas
    comme ça que ça marche.
    R.H.




    Ok, and what is tan(i + pi/2)?

    This is another complex trigonometry problem.
    That's not the point here.
    Can we please actually address the specifics?

    R.H.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Tue Jul 15 23:27:11 2025
    Op 15/07/2025 om 23:06 schreef Richard Hachel:
    Le 15/07/2025 à 22:17, sobriquet a écrit :
    Op 15/07/2025 om 17:38 schreef Richard Hachel:
    Le 15/07/2025 à 16:53, sobriquet a écrit :
    [...]
    Yes, and what is 1/i in your crackpot approach?

    Merci de bien vouloir respecter votre interlocuteur, ce mépris à la
    con devient intolérable.

    Je réponds quand même non pour vous, mais pour ceux que ça pourrait
    intéresser.

    Qu'avons nous dit? Que i n'était pas un nombre, mais un opérateur.
    Et que lorsqu'il était écrit sous forme simple i, il voulait dire
    i=1*i=-1.

    Puisque i^x=-1 quelque soit x, et que (-i)^x dépend de la parité de x. >>> Ici, on pose la question : y=1/i.

    La réponse est d'une dramatique simplicité.

    1/i=i^(-1)

    Nous venons de dire que i^x=-1 quelque soit x.

    1/i=-1

    Attention au piège, certains rigolos se sentant malins pourrait dire
    que l'on va multiplier par i les deux termes du quotient, mais c'est
    une erreur de concept. On aurait alors i/i²=-1/-1=1 SAUF QUE i est un
    opérateur, et qu'il ne sert à rien de le répéter deux fois. C'est pas >>> comme ça que ça marche.
    R.H.




    Ok, and what is tan(i + pi/2)?

    This is another complex trigonometry problem.
    That's not the point here.
    Can we please actually address the specifics?

    R.H.

    How about log(i)? Can we do that in your crackpot system?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Hachel@21:1/5 to All on Wed Jul 16 00:02:06 2025
    Le 15/07/2025 à 23:27, sobriquet a écrit :
    Op 15/07/2025 om 23:06 schreef Richard Hachel:
    Le 15/07/2025 à 22:17, sobriquet a écrit :
    Op 15/07/2025 om 17:38 schreef Richard Hachel:
    Le 15/07/2025 à 16:53, sobriquet a écrit :
    [...]
    Yes, and what is 1/i in your crackpot approach?

    Merci de bien vouloir respecter votre interlocuteur, ce mépris à la
    con devient intolérable.

    Je réponds quand même non pour vous, mais pour ceux que ça pourrait >>>> intéresser.

    Qu'avons nous dit? Que i n'était pas un nombre, mais un opérateur.
    Et que lorsqu'il était écrit sous forme simple i, il voulait dire
    i=1*i=-1.

    Puisque i^x=-1 quelque soit x, et que (-i)^x dépend de la parité de x. >>>> Ici, on pose la question : y=1/i.

    La réponse est d'une dramatique simplicité.

    1/i=i^(-1)

    Nous venons de dire que i^x=-1 quelque soit x.

    1/i=-1

    Attention au piège, certains rigolos se sentant malins pourrait dire
    que l'on va multiplier par i les deux termes du quotient, mais c'est
    une erreur de concept. On aurait alors i/i²=-1/-1=1 SAUF QUE i est un >>>> opérateur, et qu'il ne sert à rien de le répéter deux fois. C'est pas >>>> comme ça que ça marche.
    R.H.




    Ok, and what is tan(i + pi/2)?

    This is another complex trigonometry problem.
    That's not the point here.
    Can we please actually address the specifics?

    R.H.

    How about log(i)? Can we do that in your crackpot system?

    Log i = 0

    If y=Log(1) then y=0

    Log(1)=Log(-i)

    g(x)=-f(-x)+2yo

    Log i = 0

    R.H.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Wed Jul 16 03:14:00 2025
    Op 16/07/2025 om 02:02 schreef Richard Hachel:
    Le 15/07/2025 à 23:27, sobriquet a écrit :
    Op 15/07/2025 om 23:06 schreef Richard Hachel:
    Le 15/07/2025 à 22:17, sobriquet a écrit :
    Op 15/07/2025 om 17:38 schreef Richard Hachel:
    Le 15/07/2025 à 16:53, sobriquet a écrit :
    [...]
    Yes, and what is 1/i in your crackpot approach?

    Merci de bien vouloir respecter votre interlocuteur, ce mépris à la >>>>> con devient intolérable.

    Je réponds quand même non pour vous, mais pour ceux que ça pourrait >>>>> intéresser.

    Qu'avons nous dit? Que i n'était pas un nombre, mais un opérateur. >>>>> Et que lorsqu'il était écrit sous forme simple i, il voulait dire
    i=1*i=-1.

    Puisque i^x=-1 quelque soit x, et que (-i)^x dépend de la parité de x. >>>>> Ici, on pose la question : y=1/i.

    La réponse est d'une dramatique simplicité.

    1/i=i^(-1)

    Nous venons de dire que i^x=-1 quelque soit x.

    1/i=-1

    Attention au piège, certains rigolos se sentant malins pourrait
    dire que l'on va multiplier par i les deux termes du quotient, mais
    c'est une erreur de concept. On aurait alors i/i²=-1/-1=1 SAUF QUE
    i est un opérateur, et qu'il ne sert à rien de le répéter deux
    fois. C'est pas comme ça que ça marche.
    R.H.




    Ok, and what is tan(i + pi/2)?

    This is another complex trigonometry problem.
    That's not the point here.
    Can we please actually address the specifics?

    R.H.

    How about log(i)? Can we do that in your crackpot system?

    Log i = 0

    If y=Log(1) then y=0

    Log(1)=Log(-i)

    g(x)=-f(-x)+2yo

    Log i = 0

    R.H.

    But for F(x) = 5^x, you mirrored the curve in the point (x,y) = (0,1),
    because
    F(0) = 5^0 = 1

    so if we try to follow that same crackpot logic, we have an analogous
    curve f(x) = log(x) and if you try to plug in 0, we get
    f(0) = log(0) = - infinity

    https://www.wolframalpha.com/input?i=log%280%29

    So we are somehow supposed to mirror the curve for f(x) in the point
    (0, - infinity).

    --- SoupGate-Win32 v1.05
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  • From Richard Hachel@21:1/5 to All on Wed Jul 16 03:25:52 2025
    Le 16/07/2025 à 03:14, sobriquet a écrit :
    Op 16/07/2025 om 02:02 schreef Richard Hachel:

    But for F(x) = 5^x, you mirrored the curve in the point (x,y) = (0,1), because
    F(0) = 5^0 = 1

    Absolutely.


    so if we try to follow that same crackpot logic,

    No crakpot logic here.

    we have an analogous
    curve f(x) = log(x) and if you try to plug in 0, we get
    f(0) = log(0) = - infinity

    f(x)=a^x is différent that f(x)=Log x

    Here g(x) become -Log(-x) and the curve is in miroir of point $(0,0).

    f(0)=+infinity

    And f(-1)=f(i)=0

    y=Log(i)=0

    The Log (neperian) of imaginary entity i is 0.

    R.H.









    https://www.wolframalpha.com/input?i=log%280%29

    So we are somehow supposed to mirror the curve for f(x) in the point
    (0, - infinity).

    --- SoupGate-Win32 v1.05
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  • From efji@21:1/5 to All on Wed Jul 16 09:44:57 2025
    Le 16/07/2025 à 05:25, Richard Hachel a écrit :


    No crakpot logic here.

    :) :) :)


    we have an analogous curve f(x) = log(x) and if you try to plug in 0,
    we get
    f(0) = log(0) = - infinity

    f(x)=a^x is différent that f(x)=Log x

    no, kidding ?


    Here g(x) become -Log(-x) and the curve is in miroir of point $(0,0).

    theorem ?
    What about f(x) = 1+Log(x) ?
    It becomes g(x) = -(1+Log(-x)) with your "logic", right ?

    and then ?

    --
    F.J.

    --- SoupGate-Win32 v1.05
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  • From Richard Hachel@21:1/5 to All on Wed Jul 16 12:32:29 2025
    XPost: fr.sci.maths

    Le 16/07/2025 à 09:44, efji a écrit :
    Le 16/07/2025 à 05:25, Richard Hachel a écrit :

    f(x)=Log x
    Here g(x) become -Log(-x) and the curve is in miroir of point $(0,0).

    What about f(x) = 1+Log(x) ?

    g(x)=-Log(-x)+1


    It becomes g(x) = -(1+Log(-x)) with your "logic", right ?

    No.

    g(x)=-Log(-x)+1

    and then ?

    Alors votre critique est correcte, ici, puisque yo={ }, on ne peut pas utiliser 2yo.

    Ce n'est pas que ce n'est pas la bonne courbe, ni le bon résultat (c'est très simple et très mathématique
    car si on élève la courbe f(x) d'une unité la contrecourbe de l'autre
    côté s'élève aussi d'une unité).

    Mais c'est vrai que l'équation g(x)=f(-x)+yo n'est plus manipulable
    puisque yo pose ici un problème.

    Vous avez ici parfaitement raison.

    Si quelqu'un a une idée là dessus, et la façon dont il serait
    préférable d'écrire g(x), il est cordialement invité à se faire
    entendre.

    Je crosspost sur fr.sci.maths.

    R.H.

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