>>11331532You can use limits to prove this but I'll walk through the full argument instead of just invoking limits cold.
First choose any number 0 < x < 1, then there's some y = 1 - x, and y is some small positive number.
y has some decimal representation, choose enough zeros that something like .0000000000000000001 is smaller than y.
Then x < 1 - .0000000000000000001 = .9999999999999999999, which is still less than .9999999999999999999999999999999 going on forever.
So then any number you choose smaller than 1 can be proven to be strictly smaller than .999 repeating.
And I assume we can agree that .999 repeating isn't any larger than 1, so it must be equal to 1.
