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

[Bridge]

All
the proof you have is based around the flawed assertion that 1-0.9~ is
0. All of your calculations depend on this, and you provided no proof
for this assertion. Occam's Razor dictates that the explanation that
makes the least amount of unnecessary assumptions is the most efficient
and most likely correct. I am not making any assumptions by saying
1-0.9~ > 0 because 0.9~ < 1. Prove without making any assumptions how it is not.

I didn't make any assumptions.



Tell me where the assumption is.

lim n->nf {0.00 … 01} (n-1) …

Until we find a way to measure an infinitely small number(Which in practical mathematics is an absurd concept) then the definition holds true.

EXACTLY. Because there exist no rules for these types of operations at this point, the math falls apart.

How do you equate "Absurd concepts" with "no rules"?


Besides, it's been mathematically proven(See the limit above.)

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.