3 ms·
> in general even in principle mathematicians can only deal with a countable subset of the reals. So (metamathematically) if almost every single real can't actu
by tomtomtom777 6y ago
> in general even in principle mathematicians can only deal with a countable subset of the reals. So (metamathematically) if almost every single real can't actually be used in mathematics, it's hard to say the concept has much mathematical validity.
Let me give it try:
> let R be the set of real numbers. Let x be an element of R.
There it is, I've dealt with and used every single real number.
The notion that reals are only real when they are individually described (Borel's credo in the article) is an odd one. Sure, almost every real number is a "Mathematical fantasy" as the author calls it, but that doesn't mean Mathematicians can't use them or deal with them.
Mathematics excels in dealing with imaginary things. To extent Borel's credo to question the Mathematical validity of these Mathematical fantasies seems to defy the entire idea of Mathematics.