If you feel that .999... is not equal to 1, then you must be able to exhibit a number between the two of them. The rationals form a dense subset of the real line.
If the set of objects you're working with is leaves, and functions result in piles of leaves, then 1 + 1 = 1, when 2 separate piles of leaves are raked into one larger pile of leaves.
Fortunately this has nothing to do with your discussion.
ah, you qualified it though. "real line"
please, what is the exact value of the square root of -1? you cant come up with a simple single value.