> You contradict yourself: any given real number Err... I didn't say that. For good reason, as you point out. I know that you cannot "give" almost all real n

> You contradict yourself: any given real number Err... I didn't say that. For good reason, as you point out. I know that you cannot "give" almost all real numbers. I'm merely pointing out that there are mathematicians who go the extra mile and decide that those don't even exist. Symbol, name, algorithm; all of those are the same thing. And almost all real numbers (in ZFC aka "standard math") don't have one. > the TA was probably referring to the fact that the algorithm would have to stop at some point Nope, he wasn't. He specifically insisted that no amount of memory can represent pi, while any integer can be represented. He was technically correct, but I have an easier time working with pi (to any desired, even dynamically determined precision) than with Ackermann(4,4). The dimwitted TA missed the point, and he did so, because standard (not constructive) math creates lots (continuously infinitely many) of infinities, which serve no use but to make irrelevant points about things that cannot occur in actual programs.