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Transfinite induction, like regular induction, is used to show a property P(n) holds for all numbers n. The essential difference is that regular induction is restricted to ...

A sequence is an ordered set of mathematical objects. Sequences of object are most commonly denoted using braces. For example, the symbol {2n}_(n=1)^infty denotes the ...

The Walsh functions consist of trains of square pulses (with the allowed states being -1 and 1) such that transitions may only occur at fixed intervals of a unit time step, ...

Let X be an arbitrary topological space. Denote the set closure of a subset A of X by A^- and the complement of A by A^'. Then at most 14 different sets can be derived from A ...

An n-tuple, sometimes simply called a "tuple" when the number n is known implicitly, is another word for a list, i.e., an ordered set of n elements. It can be interpreted as ...

The word "order" is used in a number of different ways in mathematics. Most commonly, it refers to the number of elements in (e.g., conjugacy class order, graph order, group ...

The minimum excluded value. The mex of a set S of nonnegative integers is the least nonnegative integer not in the set.

A level set in three dimensions.

Let V be a vector space over a field K, and let A be a nonempty set. Now define addition p+a in A for any vector a in V and element p in A subject to the conditions: 1. ...

The determination of a set of factors (divisors) of a given integer ("prime factorization"), polynomial ("polynomial factorization"), etc., which, when multiplied together, ...