[hzhou321]

> but fortunately the proofs are pretty straigtforward which give a kind of «intuition» around this.

It is only straightforward once you accepted infinity and all other definitions/description based on infinity.

If you, like me, cannot accept infinity, then all the proofs/descriptions that contain infinity become apparent non-sensical.

>> Start counting the naturals: 1, 2, 3, ... >> At future timelike infinity you'll reach infinity.

This highlights the flaw. You reach infinity with infinity. Nothing is really being said about infinity. But somehow if you accepted the understanding infinity here, the rest of thesis such as cantor's diagonal argument may seem to be natural, except you forget that you really didn't know what infinity is.

All property of infinity cannot be finitely described. So anything about infinity is built on top of infinity. Turtle all the way down (or up), and we don't really know what it is.

[Dr_Segfault]

The mathematical concept of infinity generally derives from the axiom of infinity in Zermelo-Fraenkel set theory, which asserts the existence of the inductive set (which is the basis for the construction of the natural numbers). Specifically, it states that there exists a set N such that the empty set is in N, and for all x in N, x union {x} is also in N. This is an axiom, so it cannot be proven to be right or wrong. You can either accept this axiom, or attempt to create your own system of mathematics that does not require the axiom of infinity.