# 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 \(B \subseteq U\).

B. Sidney Smith , author

- [MLA] Smith, B. Sidney. "base."
*Platonic Realms Interactive Mathematics Encyclopedia.*Platonic Realms, 21 Feb 2013. Web. 21 Feb 2013. <http://platonicrealms.com/> - [APA] Smith, B. Sidney (21 Feb 2013). base. Retrieved 21 Feb 2013 from the
*Platonic Realms Interactive Mathematics Encyclopedia:*http://platonicrealms.com/encyclopedia/base/