"Chris M. Thomasson" <[email protected]> writes:

Are there "more" complex numbers than reals?

If you ask this in an appropriate group (sci.math?) I'll answer. Can
you really think this is topical in comp.lang.c?

--
Ben.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 7/8/24 6:17 PM, Chris M. Thomasson wrote:

Are there "more" complex numbers than reals? It seems so, every real has
its y, or imaginary, component set to zero. Therefore for each real
there is an infinity of infinite embedding's for it wrt any real with a non-zero y axis? Fair enough, or really dumb? A little stupid? What do
you think?

In comp.lang.c the answer is yes, for if we assume the standard 8 byte
floating point numbers, there are approximatly 2^64 possible reals
(slightly less because the encoding is not totally exhaustive) but approximately 2^128 possible complex numbers.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Mon, 8 Jul 2024 15:17:29 -0700, Chris M. Thomasson wrote:

Are there "more" complex numbers than reals?

If you talking about the theoretical mathematical sets, then the answer is
no. They can be mapped 1:1.

An obvious way to do it is to interleave the digits of the real and
imaginary parts to create a real.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 7/8/24 18:59, Ben Bacarisse wrote:

"Chris M. Thomasson" <[email protected]> writes:

Are there "more" complex numbers than reals?

If you ask this in an appropriate group (sci.math?) I'll answer. Can
you really think this is topical in comp.lang.c?

I haven't seen more of Chris's message than what you've quoted. In the
context of C, it's a easy (even trivial) question to answer.

"Each complex type has the same representation and alignment
requirements as an array type containing exactly two elements of the corresponding real type; the first element is equal to the real part,
and the second element to the imaginary part, of the complex number." (6.2.5p17).

Therefore, the number of different complex numbers that can be
represented is therefore the square of the number of different numbers
that can be represented in the corresponding real type.

The corresponding question suitable for sci.math is much trickier to answer.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

James Kuyper <[email protected]> writes:

On 7/8/24 18:59, Ben Bacarisse wrote:

"Chris M. Thomasson" <[email protected]> writes:

Are there "more" complex numbers than reals?

If you ask this in an appropriate group (sci.math?) I'll answer. Can
you really think this is topical in comp.lang.c?

I haven't seen more of Chris's message than what you've quoted. In the context of C, it's a easy (even trivial) question to answer.

"Each complex type has the same representation and alignment
requirements as an array type containing exactly two elements of the corresponding real type; the first element is equal to the real part,
and the second element to the imaginary part, of the complex number." (6.2.5p17).

Therefore, the number of different complex numbers that can be
represented is therefore the square of the number of different numbers
that can be represented in the corresponding real type.

The answer is still no, because the question is about complex
numbers and real numbers, not representable values.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 2024-07-08, Chris M. Thomasson <[email protected]> wrote:

Are there "more" complex numbers than reals? It seems so, every real has
its y, or imaginary, component set to zero. Therefore for each real
there is an infinity of infinite embedding's for it wrt any real with a non-zero y axis? Fair enough, or really dumb? A little stupid? What do
you think?

The argument is not that simple. If we restrict to just integer complex
numbers like 4 + 5i, then no; there aren't more of these than integers.
Yet the same argument about axes and embeddings could be wrongly applied.

Integer complex numbers are countable: you can start at 0, and then go
in a spiral fashion: 1, 1 + i, i, -1 + i -1, ... thus they can be put
into correspondendce with the natural numbers.

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

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 2024-07-08, Ben Bacarisse <[email protected]> wrote:

"Chris M. Thomasson" <[email protected]> writes:

Are there "more" complex numbers than reals?

If you ask this in an appropriate group (sci.math?) I'll answer. Can
you really think this is topical in comp.lang.c?

It can be. There are clearly more complex doubles than
there are doubles.

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

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Chris M. Thomasson wrote:

Are there "more" complex numbers than reals? It seems so, every real has
its y, or imaginary, component set to zero. Therefore for each real
there is an infinity of infinite embedding's for it wrt any real with a non-zero y axis? Fair enough, or really dumb? A little stupid? What do
you think?

No. You could draw a Hilbert curve (or any other space-filling curve) on
a square of the complex plane and then tile it around in a spiral to fill
up the rest of the plane. Then, you connect up all the ends of those
tiles together and pull on the ends of the curve to stretch it out to form
a line that is as infinite as the real number line.



--
Blue-Maned_Hawk│shortens to Hawk│/blu.mɛin.dʰak/│he/him/his/himself/Mr. blue-maned_hawk.srht.site
A complex plane is what's used to fly to imaginary worlds.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Kaz Kylheku <[email protected]> writes:

On 2024-07-08, Ben Bacarisse <[email protected]> wrote:

"Chris M. Thomasson" <[email protected]> writes:

Are there "more" complex numbers than reals?

If you ask this in an appropriate group (sci.math?) I'll answer. Can
you really think this is topical in comp.lang.c?

It can be. There are clearly more complex doubles than
there are doubles.

Oh come on. If the question was about C representations, why did Chris
put "more" in scare quotes? It's disingenuous to answer as if that was
the intent without first asking what Christ meant by "more" (rather than
just more).

--
Ben.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 2024-07-09, Chris M. Thomasson <[email protected]> wrote:

On 7/8/2024 3:59 PM, Ben Bacarisse wrote:

"Chris M. Thomasson" <[email protected]> writes:

Are there "more" complex numbers than reals?

If you ask this in an appropriate group (sci.math?) I'll answer. Can
you really think this is topical in comp.lang.c?

Ahhhh shit! this was meant for sci.math! Damn it! Cursing, ..., ..., .....

Anyway, a complex number is a + ib where a and b are real.

We can take any two reals (wlog, in the range [0, 1)):

a = 0 . a0 a1 a2 a3 a4 .... (a0 a1 ... are decimal digits of a)

b = 0 . b0 b1 b2 b3 b4 ....

and intertwine the digits to make a new real number:

c = 0. a0 b0 a1 b1 a2 b2 ...

That new number c is still among the reals.

The intertwining is undoable: you can recover the original pair
of numbers by taking the even or odd digits.

Thus, any complex number can be encoded as a real number,
which implies that there can't be more of them than reals.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 09/07/2024 1

put "more" in scare quotes? It's disingenuous to answer as if that was
the intent without first asking what Christ meant by "more" (rather than
just more).

Fish? Bread? Maybe Wine?

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Richard Harnden <[email protected]d> writes:

On 09/07/2024 1

put "more" in scare quotes? It's disingenuous to answer as if that was
the intent without first asking what Christ meant by "more" (rather than
just more).

Fish? Bread? Maybe Wine?

Ha! An unusual typo for me. Given the way I see words, I had to read
it quite a few times before I saw it, even with your comment.

--
Ben.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 7/9/24 05:04, Ben Bacarisse wrote:

Kaz Kylheku <[email protected]> writes:

On 2024-07-08, Ben Bacarisse <[email protected]> wrote:

"Chris M. Thomasson" <[email protected]> writes:

Are there "more" complex numbers than reals?

If you ask this in an appropriate group (sci.math?) I'll answer. Can
you really think this is topical in comp.lang.c?

It can be. There are clearly more complex doubles than
there are doubles.

Oh come on. If the question was about C representations, why did Chris
put "more" in scare quotes? It's disingenuous to answer as if that was
the intent without first asking what Christ meant by "more" (rather than
just more).

It may be disingenuous, but deliberately misinterpreting his question as
if it had been one that would be on-topic in this newgroup is an
entirely appropriate way of reminding him that his question was off-topic.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Tue, 9 Jul 2024 12:00:29 -0700, Chris M. Thomasson wrote:

By the way, did you take a look at my "fun"
experiment wrt storing data in the roots of complex numbers?

You can encode messages in anything.

#!/usr/bin/python3

import sys

charset = ' .Hadefghilmnoprstwx'
modulo = 23
s = 1193321429126088671017703197607273471738040746714878246039040663141374779777444615292185709614467374016367591074170680369683264762098941
num = iter(range(2, 9999))
while s != 1 :
n = next(num)
if s % n == 0 :
sys.stdout.write("%s" % charset[(n - 1) % modulo])
s //= n
#end if
#end while
sys.stdout.write("\n")

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Wed, 10 Jul 2024 15:42:14 -0700, Chris M. Thomasson wrote:

Integer complex numbers ...

Another fun thing about integer complex numbers is that some numbers that
are primes if you stay on the real line, become non-prime if complex
integer factors are allowed.

E.g.

5 = (2 + i)(2 - i)
29 = (5 + 2i)(5 - 2i)
101 = (10 + i)(10 - i)

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)