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  • Infinitesimals don't exist

    From Mr Flibble@21:1/5 to All on Mon Aug 25 02:53:17 2025
    Much like infinitesimals, Olcott's refutations of the Halting Problem
    proofs don't exist.

    /Flibble



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  • From Richard Damon@21:1/5 to Mr Flibble on Mon Aug 25 07:09:26 2025
    On 8/24/25 10:53 PM, Mr Flibble wrote:
    Much like infinitesimals, Olcott's refutations of the Halting Problem
    proofs don't exist.

    /Flibble




    But they surely do exist in the fields that define them.

    That they don't exist in some systems that are more restrictive, doesn't
    mean they don't exist.

    They aren't part of the "Real Numbers", but that is just like Pi doesn't
    exist in the integers, but does exist, or "i" exists in the Complex
    Numbers, but not the "Real Numbers".

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  • From Richard Heathfield@21:1/5 to Mikko on Tue Aug 26 10:44:52 2025
    On 26/08/2025 10:40, Mikko wrote:
    On 2025-08-25 02:53:17 +0000, Mr Flibble said:

    Much like infinitesimals, Olcott's refutations of the Halting
    Problem
    proofs don't exist.

    That you can't see infinitesimals does not mean that they don't
    exist.


    On the other hand, that you can't see invisible pink unicorns is
    proof positive that they /do/ exist.

    Ever seen one?

    Exactly!

    --
    Richard Heathfield
    Email: rjh at cpax dot org dot uk
    "Usenet is a strange place" - dmr 29 July 1999
    Sig line 4 vacant - apply within

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  • From Mikko@21:1/5 to Mr Flibble on Tue Aug 26 12:40:05 2025
    On 2025-08-25 02:53:17 +0000, Mr Flibble said:

    Much like infinitesimals, Olcott's refutations of the Halting Problem
    proofs don't exist.

    That you can't see infinitesimals does not mean that they don't exist.
    It only means that if they exist they are too small to be seen.

    --
    Mikko

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  • From Mr Flibble@21:1/5 to Mikko on Tue Aug 26 17:29:03 2025
    On Tue, 26 Aug 2025 12:40:05 +0300, Mikko wrote:

    On 2025-08-25 02:53:17 +0000, Mr Flibble said:

    Much like infinitesimals, Olcott's refutations of the Halting Problem
    proofs don't exist.

    That you can't see infinitesimals does not mean that they don't exist.
    It only means that if they exist they are too small to be seen.

    False, there is always a number smaller than the value of a claimed infinitesimal.

    /Flibble


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  • From Kaz Kylheku@21:1/5 to Mr Flibble on Tue Aug 26 21:31:57 2025
    On 2025-08-26, Mr Flibble <[email protected]> wrote:
    On Tue, 26 Aug 2025 12:40:05 +0300, Mikko wrote:

    On 2025-08-25 02:53:17 +0000, Mr Flibble said:

    Much like infinitesimals, Olcott's refutations of the Halting Problem
    proofs don't exist.

    That you can't see infinitesimals does not mean that they don't exist.
    It only means that if they exist they are too small to be seen.

    False, there is always a number smaller than the value of a claimed infinitesimal.

    Therefore, an infinitesimal has to be something which is not
    (that kind of) a number. A positive infinitesimal is something outside of
    the real numbers which is closer to zero than any positive real.

    You can just postulate the existence of such a thing as an axiom,
    and see where that goes.

    --
    TXR Programming Language: http://nongnu.org/txr
    Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
    Mastodon: @[email protected]

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  • From Mr Flibble@21:1/5 to Chris M. Thomasson on Tue Aug 26 23:53:59 2025
    On Tue, 26 Aug 2025 13:21:16 -0700, Chris M. Thomasson wrote:

    On 8/26/2025 10:29 AM, Mr Flibble wrote:
    On Tue, 26 Aug 2025 12:40:05 +0300, Mikko wrote:

    On 2025-08-25 02:53:17 +0000, Mr Flibble said:

    Much like infinitesimals, Olcott's refutations of the Halting Problem
    proofs don't exist.

    That you can't see infinitesimals does not mean that they don't exist.
    It only means that if they exist they are too small to be seen.

    False, there is always a number smaller than the value of a claimed
    infinitesimal.

    Indeed. .1, .01, .001, .001, .0001, ...

    limit 0.

    We can see the steps, and we know its limit is 0 wrt infinity. Looking
    at it all the way down, we will never see an iteration as perfectly
    equal to its limit... Fair enough?

    I was talking about infinitesimals not limits: they are different concepts
    (in fact limits supplanted infinitesimals in 19th century calculus).

    /Flibble



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  • From Andy Walker@21:1/5 to Mr Flibble on Wed Aug 27 01:18:28 2025
    On 27/08/2025 00:53, Mr Flibble wrote:
    I was talking about infinitesimals not limits: they are different concepts (in fact limits supplanted infinitesimals in 19th century calculus).

    Indeed, but infinitesimals came back in the 20thC, in the forms
    of (a) non-standard analysis, (b) surreal numbers, and (c) [combinatorial] games. Before people write complete nonsense on the subject, I suggest
    that at least they should wiki those topics. They aren't particularly difficult, and they're very interesting [at least to mathematicians].

    --
    Andy Walker, Nottingham.
    Andy's music pages: www.cuboid.me.uk/andy/Music
    Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Spindler

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  • From Richard Damon@21:1/5 to Mr Flibble on Tue Aug 26 21:49:06 2025
    On 8/26/25 1:29 PM, Mr Flibble wrote:
    On Tue, 26 Aug 2025 12:40:05 +0300, Mikko wrote:

    On 2025-08-25 02:53:17 +0000, Mr Flibble said:

    Much like infinitesimals, Olcott's refutations of the Halting Problem
    proofs don't exist.

    That you can't see infinitesimals does not mean that they don't exist.
    It only means that if they exist they are too small to be seen.

    False, there is always a number smaller than the value of a claimed infinitesimal.

    /Flibble



    Are you sure?

    What value is smaller that delta in the number system of infinitesimals,
    where all infinitesimals are multiples of delta.

    They work sort of like the integers, being spaced apart.


    Just as there is no integer between 0 and 1, there is no infinitesimal
    between 0 and delta.

    Note, once you introduce the term infinitesimal, you are allowing the
    space they are defined in.

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  • From Mr Flibble@21:1/5 to Richard Damon on Wed Aug 27 01:52:19 2025
    On Tue, 26 Aug 2025 21:49:06 -0400, Richard Damon wrote:

    On 8/26/25 1:29 PM, Mr Flibble wrote:
    On Tue, 26 Aug 2025 12:40:05 +0300, Mikko wrote:

    On 2025-08-25 02:53:17 +0000, Mr Flibble said:

    Much like infinitesimals, Olcott's refutations of the Halting Problem
    proofs don't exist.

    That you can't see infinitesimals does not mean that they don't exist.
    It only means that if they exist they are too small to be seen.

    False, there is always a number smaller than the value of a claimed
    infinitesimal.

    /Flibble



    Are you sure?

    What value is smaller that delta in the number system of infinitesimals, where all infinitesimals are multiples of delta.

    They work sort of like the integers, being spaced apart.


    Just as there is no integer between 0 and 1, there is no infinitesimal between 0 and delta.

    Note, once you introduce the term infinitesimal, you are allowing the
    space they are defined in.

    I am talking about real numbers but of course you know this as you are a disingenuous f--k.

    /Flibble



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  • From Richard Damon@21:1/5 to Mr Flibble on Tue Aug 26 22:00:23 2025
    On 8/26/25 9:52 PM, Mr Flibble wrote:
    On Tue, 26 Aug 2025 21:49:06 -0400, Richard Damon wrote:

    On 8/26/25 1:29 PM, Mr Flibble wrote:
    On Tue, 26 Aug 2025 12:40:05 +0300, Mikko wrote:

    On 2025-08-25 02:53:17 +0000, Mr Flibble said:

    Much like infinitesimals, Olcott's refutations of the Halting Problem >>>>> proofs don't exist.

    That you can't see infinitesimals does not mean that they don't exist. >>>> It only means that if they exist they are too small to be seen.

    False, there is always a number smaller than the value of a claimed
    infinitesimal.

    /Flibble



    Are you sure?

    What value is smaller that delta in the number system of infinitesimals,
    where all infinitesimals are multiples of delta.

    They work sort of like the integers, being spaced apart.


    Just as there is no integer between 0 and 1, there is no infinitesimal
    between 0 and delta.

    Note, once you introduce the term infinitesimal, you are allowing the
    space they are defined in.

    I am talking about real numbers but of course you know this as you are a disingenuous f--k.

    /Flibble


    Then the word "infintesimal" isn't defined, so you can't talk about them.

    Or are you saying someone can say that 0.5 doesn't exist, because they
    were talking about the integers WITHOUT SAYING SO,

    Yes, infinitesimals don't exist in the Real Number System, but then so
    doesn't infinity, or sqrt(-1), both of which are also concepts that
    exist in extensions of the system.

    The, the statement "Infintesimals don't exist" without a clear
    indication that you mean to work in the Real Number system is just a lie.

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  • From Kaz Kylheku@21:1/5 to Mr Flibble on Wed Aug 27 06:05:40 2025
    On 2025-08-27, Mr Flibble <[email protected]> wrote:
    On Tue, 26 Aug 2025 21:49:06 -0400, Richard Damon wrote:
    Note, once you introduce the term infinitesimal, you are allowing the
    space they are defined in.

    I am talking about real numbers but of course you know this as you are a disingenuous f--k.

    Now you're just farting and lighting a match, while trying to use subtle psychological tricks to make everyone believe you're gaslighting.

    If only everyone would pay attention to what you're SAYING instead
    of obsessively focusing on assuming that you must be wrong ...

    --
    TXR Programming Language: http://nongnu.org/txr
    Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
    Mastodon: @[email protected]

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