>>11052098Suppose 0.99... is strictly less than 1
Therefore 1-0.99... =x where x is strictly greater than 0.
So 1-x=0.99...
Now let's consider 1-0.1x, this expression is at least as large as 1-x, but definitely smaller than 1. So, either it's 1-x<1-0.1x<1 or 1-x=1-0.1x<1. If 1-x=1-0.1x then x=0 which is a contradiction. If 1-x is less than 1-0.1x, then there exists a number between 0.99... and 1, which will call y. Y must be strictly smaller than 1 and strictly larger than 0.99... so there exists numbers 1-Y and Y-0.99.. that sum to x. These numbers must be stricty nonzero and smaller than x, and their absolute difference must be smaller than either, call it z so that 1-z is greater than 1-y and greater than 1-x. You can do this forever and find an infinite amount of numbers larger than 0.99.. and smaller than 1. So either 0.99... is equal to 1 or it's totally meaningless because there's always a number closer to 1 than it.
