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Always increasing; never remaining constant or decreasing. Also called strictly increasing.

A sequence {a_n} such that either (1) a_(i+1)>=a_i for every i>=1, or (2) a_(i+1)<=a_i for every i>=1.

A basis, form, function, etc., in two or more variables is said to be multilinear if it is linear in each variable separately.

A function f:A->B such that B is a set of numbers.

A mathematical object upon which an operator acts. For example, in the expression 1×2, the multiplication operator acts upon the operands 1 and 2.

A function that exhibits oscillation (i.e., slope changes) is said to be oscillating, or sometimes oscillatory.

Functions which have derivatives of all orders at all points and which, together with their derivatives, fall off at least as rapidly as |x|^(-n) as |x|->infty, no matter how ...

The image of the path gamma in C under the function f is called the trace. This usage of the term "trace" is unrelated to the same term applied to matrices or tensors.

A point x_0 is said to be a periodic point of a function f of period n if f^n(x_0)=x_0, where f^0(x)=x and f^n(x) is defined recursively by f^n(x)=f(f^(n-1)(x)).

An integral which is equivalent to the Denjoy integral "in the restricted sense."