Given integers a and b and the relation a <= b, intuitively I feel I can transform this inequality into a strict inequality like this:
a < b + 1
Conversely, I should be able to transform the strict inequality a < b to a non-strict one like this:
a + 1 <= b
My question is, is there any way I can do the same transformations if a and b are real numbers, WITHOUT introducing some kind of slack/surplus variables? I.e. is there a way to do the transformation by only using constants? I do not feel that it should be possible due to the nature of the real numbers, but I would just like to find out.