[split] 0.999... equals 1

[edk]

I have already shown one equation in which 0.999... and 1.000... are not interchangeable. The problem is infinity and we just need a better way to handle infinities.

(Technically, all numbers are infinitely long, but we will stick with tradition and consider any infinitely long number that does not end in zero.)

Take for instance this 'infinite' set -> ( 0.1, 0.01, 0.001, ...) in which only the last number is 'infinitely long' (in the set of transcendentals, all numbers are 'infinitely' long. )

The "last' number would be 0.000...1, ..........

Which equation?

If there are infinite zeroes and then a 1, there is no 1. What would the smallest number larger than 0.0...1 be? Are numbers preceded by an infinite number of zeroes even ordered? Any of these numbers with infinite zeros followed by some other numbers is simultaneously equal to itself, larger than itself and smaller than itself, which doesn't sound much like a number to me.