3 ms·
How real is an imaginary number? Best to think of them as mathematical constructs and not get too hung up on them IMHO.
by Rapzid 4y ago
How real is an imaginary number? Best to think of them as mathematical constructs and not get too hung up on them IMHO.
- marginalia_nu 4y agoWhat does it mean for a number to be real (in the lower case sense of the word)?
- lupire 4y agoImaginary numbers are more real than transcendental "real" numbers, and much more real than the unnameable reals, which are almost every real. It's easy to set up situation that points to any algebraic complex number.
- scapp 4y ago> the unnameable reals, which are almost every real Is there a definition you have in mind for "unnameable"? If you mean definable [0][1], then this is independent of ZFC. The "standard" argument for this is flawed, and indeed there are models where every real is definable. [2] [0] "x is definable if there exists a first order formula with one free variable P such that x is the unique real number with P(x) true" [1] https://en.wikipedia.org/wiki/Definable_real_number#Definability_in_models_of_ZFC https://en.wikipedia.org/wiki/Definable_real_number#Definabi... [2] https://mathoverflow.net/questions/44102/is-the-analysis-as-taught-in-universities-in-fact-the-analysis-of-definable-numb/44129#44129 https://mathoverflow.net/questions/44102/is-the-analysis-as-...
- floxy 4y agoMaybe the GP is referring to something like Chapter 5 of Chaitin's Meta Math!. https://arxiv.org/pdf/math/0404335.pdf https://arxiv.org/pdf/math/0404335.pdf
- bawolff 4y agoWhat does imaginary numbers have to do with the topic at hand?
- Rapzid 4y agoIt's a play on words.