During my trying to do assignment 2, I stumbled into a nice way of restating stuff like x + y. Actually y can be a variable or an integer. The following is just a sketch that can prove useful; it assumes y is a variable:
To make it easier, [x] means floor of x
x + y = x + [x] -[x] + y + [y] - [y]
= x-{x}+ y - {y] + [x] + [y]
but x - [x] < 1. the same for y (from class notes)
Therefore: x + y < [x] +[y] + 2
How is this useful?
Thy this on the limit proof on the assignment to set d as a function of epsilon.
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