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> we can not faithfully order a mix of Real and Complex numbers A mix of real and complex numbers is just a set of complex numbers, because every real number
by etatoby 10y ago
> we can not faithfully order a mix of Real and Complex numbers
A mix of real and complex numbers is just a set of complex numbers, because every real number is a complex number. And complex numbers do not possess a total ordering: https://proofwiki.org/wiki/Complex_Numbers_cannot_be_Totally_Ordered https://proofwiki.org/wiki/Complex_Numbers_cannot_be_Totally...
- JadeNB 10y ago> complex numbers do not possess a total ordering The set of complex numbers does not possess a total ordering that respects the algebraic operations. The set of complex numbers is in bijection (in many, meaningless, ways) with the set of real numbers, and so certainly admits a (indeed many, meaningless) total ordering.