Max

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

max((Subscript[x, 1]),(Subscript[x, 2]),…) is the numerically largest of the real numbers (Subscript[x, k]).

max((Subscript[z, 1]),(Subscript[z, 2]),…) is not defined for complex numbers (Subscript[z, k]).

Specific values

Specialized values

Values at fixed points

Values at infinities

General characteristics

Domain and analyticity

max is real valued function of an arbitrary number of real variables. In (ℝ^n) it is a piecewise linear function. The derivative of max((Subscript[x, 1]),(Subscript[x, 2]),…,(Subscript[x, k]),…,(Subscript[x, j]),…,(Subscript[x, n])) is discontinuous at (Subscript[x, j])==(Subscript[x, k]) for all j,  k.

Symmetries and periodicities

Permutation symmetry

Periodicity

No periodicity

Sets of discontinuity

The function max((Subscript[x, 1]),(Subscript[x, 2]),…,(Subscript[x, n])) is continuous function in (ℝ^n).

Limit representations

Transformations

Transformations and argument simplifications

Identities

Functional identities

Complex characteristics

Real part

Imaginary part

Absolute value

Argument

Conjugate value

Summation

Integral transforms

Fourier exp transforms

Laplace transforms

Representations through more general functions

Through other functions

Representations through equivalent functions

History

The function max is encountered often in mathematics and the natural sciences.

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