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Numerical Functions
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.
Round  ▪ Floor  ▪ Ceiling  ▪ IntegerPart  ▪ FractionalPart
Min, Max minimum or maximum of numbers or lists
Abs absolute value
Sign sign (-1, 0, +1)
Clip clip to between -1 and +1 or other limits
Rescale rescale to run between 0 and 1
Chop chop small values to 0
Unitize 0 for x=0, and 1 otherwise
UnitStep 0 for x<0, and 1 for x0
Piecewise general piecewise function
Boole 1 for True, 0 for False
DiscreteIndicator indicator function for a discrete set
Less(< ▪ Greater(> ▪ LessEqual(<= ▪ GreaterEqual (>=)
IntegerQ test whether an expression is an integer
Mod  ▪ Quotient  ▪ GCD  ▪ ...