Mathematics. Dictionary

Odd function · O

Any function whose value changes sign if the independent variable changes sign i.e. f(-x) = -f(x)

Open interval · O

An interval in the real number line which does not contain its supremum and infimum. If specified by a pair of real numbers, then it consists of all the points on the real line whose values lie strictly between those two real numbers.

Open set · O

Informally, a set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary.

Operator theory · O

A branch of functional analysis, being the study of linear operators on function spaces.

Ordered pair · O

An object containing exactly two elements in a fixed order, so that, when the elements are different, exchanging them gives a different object. Notation: (a, b) or \langle a, b\rangle.

Ordinal number · O

A natural number used to denote position in a sequence.

Ordinary differential equation · O

An equation involving the derivatives of a function of only one independent variable.

Orthogonal complement · O

The set of all vectors which are orthogonal to a given set of vectors.

Orthogonal matrix · O

A square matrix whose columns, considered as vectors, are orthonormal to each other. This implies that the transpose of such a matrix is also its inverse.