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

[Bridge]

When I say "infinitely small" I don't actually mean with an infinite amount of decimal places, I mean unmeasurable at this point.

Here is the Wikipedia definition of "infinitesimal":

"In common speech, an infinitesimal object is an object which is
smaller than any feasible measurement, but not zero in size; or, so
small that it cannot be distinguished from zero by any available means.
Hence, when used as an adjective, "infinitesimal" in the vernacular
means "extremely small". An infinitesimal object by itself is often
useless and not very well defined; in order to give it a meaning it
usually has to be compared to another infinitesimal object in the same
context (as in a derivative) or added together with an extremely large (an infinite) amount of other infinitesimal objects (as in an integral)."

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.