First-order language
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A First-order language in Zermelo-Fraenkel set theory consists of the following symbols:
- A set of constants, such as A, B, C, ...
- A set of n-ary relations such as >(x, y).
- A set of n-ary functions such as +(x, y).
- An infinite set of variables such as x, y, z,...
- The connectives <math>\neg</math>, <math>\wedge</math>.
- quantifiers: <math>\forall</math>, <math>\exists</math>.
- parenthesis: <math>(</math>, <math>)</math>.
- The equality symbol <math>=</math>.
First-order languages are used to describe mathematics in mathematical notation with mathematical formulae.