Re: Incompleteness of Cantor's enumeration of the rational numbers (doubling-spaces)

Am 13.11.2024 um 03:37 schrieb Chris M. Thomasson:

[...] It's fun that all real numbers are complex numbers but not all complex numbers are real numbers...

Actually, this is a quite fascinating state of affairs. (In math there's a whole (and rather important) "branch" which relies on complex numbers: "function theory" or "complex analysis".*)
Many technical "approaches" (say in electrical engineering or physics) DEPEND on complex numbers.
In fact, there's something quite remarkable in connection with quantum theory: https://www.nature.com/articles/s41586-021-04160-4
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*) "Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering." (Wikipedia)