>>12606767>And you know such a process, but I don't, is your point?Yeah, you just take an arbitrary number that suits your fancy. Let me do it right now. I pick 0.133555126222

>That is absolutely correct. I can tell that you know a lot about shit.The point is that measure theory tells you absolutely nothing that would ever be empirically relevant.

>That is totally irrelevant to what is written on the nice looking lady's blackboardIt is relevant. A mathematician uses words like "almost every" that sound meaningful when in reality they tell you absolutely nothing beyond the purely, meaningless formalism of shuffling formulas around.

>Your hobby is to move goalposts? I didn't move goalposts even once. You sound confused.

>Let us say that P(x) is the statement that x is irrational. Then P is true almost always. This implies that there exists a number x that is irrational. This is verified empirically(?) by verifying that the longest side of an isosceles right triangle with two sides of length 1/2 has irrational length.This is a good example of the type of reasoning that is a complete nonsequitur. Just because some property P holds for almost all numbers has absolutely nothing to do with how likely you are to find an example of a number with property P, and your example is a pure coincidence. It's like saying "Jane said 13543 is quite an odd number and that empirically verifies the fact that 13543 is odd (not divisible by 2)". A total confusion of language.

>But of course I have no actual idea what you mean by verifying experimentally the properties of abstract notionsLike literally everything to do with statistics. Experiments like Buffon's needle that let you calculate pi. The claim that there are infinitely many twin primes translates to the empirical claim that an algorithm that looks for twin primes will always find another one. Riemann hypothesis translates to the claim that an algorithm that looks for nontrivial zeros will only find them on the line Re=1/2.