# 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 $$B \subseteq U$$.