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I don't understand that argument. But in any case, Cantor's argument is very constructive. It literally gives you the decimal expansion of the new number not in
by OscarCunningham 7y ago
I don't understand that argument. But in any case, Cantor's argument is very constructive. It literally gives you the decimal expansion of the new number not in your set.
- solinent 7y agoI didn't do it that much justice because I was discovering it independently, my arguments can easily be made rigorous, but you'd need a background in pure mathematics to understand it. However, there's a section on Wiki: https://en.wikipedia.org/wiki/Definable_real_number#Definability_in_models_of_ZFC https://en.wikipedia.org/wiki/Definable_real_number#Definabi... They start with a stronger definition of a definable number, so they find that they do exist. I think given the argument above there must be a hole in my own argument, I'd have to go beyond ZFC.