Throughout
Mathematica there is support not only for approximate real numbers, but also for exact numbers represented in algebraic or symbolic form. Functions like
Floor,
IntegerPart and
Max are all in effect set up to "prove theorems"—often using original algorithms developed at Wolfram Research—to give values with exact inputs.
Min,
Max — minimum or maximum of numbers or lists
Clip — clip to between -1 and +1 or other limits
Rescale — rescale to run between 0 and 1
Piecewise — general piecewise function
IntegerQ — test whether an expression is an integer
