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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: More complex numbers than reals?
Date: Sat, 13 Jul 2024 22:55:13 -0000 (UTC)
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Am Fri, 12 Jul 2024 17:13:09 +0000 schrieb WM:
> Le 11/07/2024 à 02:46, Ben Bacarisse a écrit :
>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
> 
>>> {a, b, c} vs { 3, 4, 5 }
>>> Both have the same number of elements,
>> That will fall down for infinite sets unless, by decree, you state that
>> your meaning of "more" makes all infinite sets have the same number of
>> elements.
> There are some rules for comparing sets which are not subset and
> superset, namely symmetry:
> The real numbers in intervals of same length like (n, n+1] are
> equinumerous.
What is their number?
In fact every interval contains uncountably many numbers.
Of course you can assign this the useless measure 1.

> Further there is a rule of construction: The rational numbers are |ℚ| =
> 2|ℕ|^2 + 1.
No, they are countable: bijective to the naturals.
And what would this expression mean if you can't manipulate it?
> The real numbers are infinitely more than the rational numbers because
> every rational multiplied by an irrational is irrational.

> Of course the complex numbers are infinitely many more than the reals.
> That's the subset rule.
> These rules have not lead to any contradiction, to my knowledge. Please
> try.
Consider the set of even numbers. Clearly they are bijective to the
naturals, yet a subset of them. How many are there?

-- 
Am Fri, 28 Jun 2024 16:52:17 -0500 schrieb olcott:
Objectively I am a genius.