Wait what? (1+2+3+4+...

[Froge]

Why then do you accept illogical data that is the result of making calculations in systems that do not support said calculations?

0.999... is not a number with nonzero decimals, despite how it looks when it is written. A basic principle of mathematics is that there is some distance, no matter how infinitesimal, between any two different numbers. For example, there are an infinite quantity of numbers between 0.99 and 1 (eg. 0.991, 0.9999992, etc.) However, there is absolutely no distance between 0.999... and 1 because the 9s go on to infinity.

Fundamentally, you have to realize that the 9s simply do not stop. You cannot assume "oh, even after you go on for a really long time eventually the 9s end" because that is not the definition of infinity. Infinity is a concept defined by that "if there is a number, infinity is larger." So even the largest numbers ever conceived (example: graham's number) are infinitely small compared to infinity. That means no matter how you try, you absolutely cannot find a value between 0.999... and 1.

Think of 0.999... as just a different way of writing 1. It is an application of the concept of infinity.