# base

### Arithmetic

In a place-notational number system, the *base* is the number of symbols used. For instance, in binary or base-2 notation, only the two symbols 0 and 1 are used, whereas in octal or base-8 notation the eight symbols 0, 1, 2, 3, 4, 5, 6, and 7 are used.

In exponential notation the *base* is the number that is being ‘raised to the power of’ the exponent.

### Topology

Given a topological space \(X\), a *base* for \(X\) is a class \(ℬ\) of subsets of \(X\) such that \(\forall x \in X\) and every neighborhood \(U\) of \(x\), there is a set \(B \in ℬ\) such that \(x \in B\) and \(B \subseteq U\).