First-order language

A First-order language in Zermelo-Fraenkel set theory consists of the following symbols:

1. A set of constants, such as A, B, C, ...
2. A set of n-ary relations such as >(x, y).
3. A set of n-ary functions such as +(x, y).
4. An infinite set of variables such as x, y, z,...
5. The connectives <math>\neg</math>, <math>\wedge</math>.
6. quantifiers: <math>\forall</math>, <math>\exists</math>.
7. parenthesis: <math>(</math>, <math>)</math>.
8. The equality symbol <math>=</math>.

First-order languages are used to describe mathematics in mathematical notation with mathematical formulae.