I 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 mathe

I 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.