Re: More complex numbers than reals?

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.