[ummonk]

You're assuming you've been able to construct all those real numbers in the first place, using arbitrary imaginary cauchy sequences (i.e. cauchy sequences that cannot be constructed but rather rely on some magic axiom of infinite choice).

[papandada]

Such an interesting criticism. All of this thread has been enlightening. I sat through traditional undergrad analysis and set theory classes and never imagined there was another option, other than things bothering me for decades since in my subconscious.