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Re:An intutive counterexample to the axiom of choice by mannerheim on Monday January 23, 2023 @11:11AM (#34490635)
There are uncomputable numbers which can still be defined.

https://en.wikipedia.org/wiki/Chaitin%27s_constant

Re:An intutive counterexample to the axiom of choice by Beldin on Tuesday January 24, 2023 @01:46AM (#34500245)
See also this Numberphile video on numbers, including algebraic, computable, transcendental, and talking about numbers beyond those.

https://m.youtube.com/watch?v=5TkIe60y2GI