>>12576478"Uncomputable numbers" is one of the best illustration of the silliness that is real numbers. When mathematicians talk about such surprising unconventional things as uncomputable numbers, it is very good to get down to the basics and see what is actually meant by a number. If you look at the definitions carefully, you'll realize that it's actually a meaningless undefined concept. All of mathematics, according to the modern paradigm, is just manipulation of formal strings which don't necessarily represent anything. So what mathematicians call a number is just a formula in logic which under the intuitive interpretation expresses the existence of some infinite, infinitely complex set which no one knows anything about.
And if you ask mathematicians why they think uncomputable numbers exist they will always present some argument that either depends on unjustified purely formal axioms of "set theory" which don't have any correlation to reality, or they will resort to arguments which require infinite amount of work. For example, given an algorithm to calculate whether that algorithm represents a computable number, and do that for ALL algorithms, clearly an impossible task even in principle, to perform a cantor-like diagonal argument and allegedly produce a "number" which no one knows anything about.
