Re: More complex numbers than reals?

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.
Further there is a rule of construction: The rational numbers are |ℚ| = 2|ℕ|^2 + 1.
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.
Regards, WM