Numerical Functions

IntegerPart[x]integer part of x
FractionalPart[x]fractional part of x
Round[x]integer x closest to x
Floor[x]greatest integer x not larger than x
Ceiling[x]least integer x not smaller than x
Rationalize[x]rational number approximation to x
Rationalize[x,dx]rational approximation within tolerance dx

Functions relating real numbers and integers.

xIntegerPart[x]FractionalPart[x]Round[x]Floor[x]Ceiling[x]
2.420.4223
2.520.5223
2.620.6323
-2.4-2-0.4-2-3-2
-2.5-2-0.5-2-3-2
-2.6-2-0.6-3-3-2

Extracting integer and fractional parts.

IntegerPart[x] and FractionalPart[x] can be thought of as extracting digits to the left and right of the decimal point. Round[x] is often used for forcing numbers that are close to integers to be exactly integers. Floor[x] and Ceiling[x] often arise in working out how many elements there will be in sequences of numbers with noninteger spacings.

Sign[x]1 for x>0, -1 for x<0
UnitStep[x]1 for x0, 0 for x<0
Abs[x]absolute value x of x
Clip[x]x clipped to be between 1 and +1
Rescale[x,{xmin,xmax}]x rescaled to run from 0 to 1
Max[x1,x2,] or Max[{x1,x2,},]
the maximum of , ,
Min[x1,x2,] or Min[{x1,x2,},]
the minimum of , ,

Numerical functions of real variables.

x+Iythe complex number
Re[z]the real part TemplateBox[{Re, paclet:ref/Re}, RefLink, BaseStyle -> InlineFormula] z
Im[z]the imaginary part TemplateBox[{Im, paclet:ref/Im}, RefLink, BaseStyle -> InlineFormula] z
Conjugate[z]the complex conjugate or
Abs[z]the absolute value z
Arg[z]the argument such that

Numerical functions of complex variables.