1 = 0,99........

[Ghieri]

Because we have no way of measuring numbers that small at this point in
time. The difference between 0.9~ and 1 is immeasurably small, but it
still exists. I don't consider it proven because the arithmetic
operators +, -, * and / are designed to work with measurable numbers. As soon as you start using numbers that have no definite value the math stops working.

I think you misunderstand, "infinitely small", "infinite", etc are not actual numbers. You can measure numbers. You cannot count to infinity, or measure infinite anything. There is no countable distance between .99~ and 1. It is not that we cannot measure infinity "Yet", it's that infinity is immeasurable by nature. It only exists because theoretically, there is no natural upper limit of numbers.

An infinitely small number is not an actual number, because you can continuously divide the number and it will only get smaller and smaller. It does not, by definition, have a value, because you cannot reach the value, or plug it into an equation. It's on the same level as "undefined". Something that exists in mathematics as a way to tell the mathematician they are doing something wrong. Does that make sense?