Numerical Functions
Throughout the Wolfram Language 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
MixedFractionParts — integer and fractional parts of a mixed fraction
Min, Max — minimum, maximum of numbers or lists
RealAbs — absolute value of real numbers
RealSign — sign of real numbers (
, 
, 
)
Abs — absolute value of complex numbers
Sign — sign of complex numbers
Clip — clip to between 
and 
or other limits
Rescale — rescale to run between 
and 
Chop — chop small values to 
Threshold — set values in a list below a threshold to 0.
LogisticSigmoid — sigmoid function
Unitize — 0 for x0, and 1 otherwise
UnitStep — 0 for x<0, and 1 for x≥0
Ramp — 
for 
, and 
for 
Piecewise — general piecewise function
Boole — 1 for True, 0 for False
DiscreteIndicator — indicator function for a discrete set
Less(<) ▪ Greater(>) ▪ LessEqual(<=) ▪ GreaterEqual (>=)
NumericalOrder — give -1, 0, +1 for less, equal, greater
SquareWave ▪ TriangleWave ▪ SawtoothWave
Integer Functions »
IntegerQ — test whether an expression is an integer
Mod ▪ Quotient ▪ GCD ▪ ModularInverse ▪ ...