Changes

A '''First-order language''' consists of the following symbols:

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 [[constant]]s, such as ''A'', ''B'', ''C'', ...

#A set of n-ary relations such as ''>(x, y)''.

#A set of n-ary [[relation]]s such as ''>(x, y)''.

#A set of n-ary functions such as ''+(x, y)''.

#A set of n-ary [[function]]s such as ''+(x, y)''.

#An [[infinite]] set of variables such as ''x'', ''y'', ''z'',...

#An [[infinite]] set of variables such as ''x'', ''y'', ''z'',...

#The connectives <math>\neg</math>, <math>\wedge</math>.

#The connectives <math>\neg</math>, <math>\wedge</math>.

#quantifiers: <math>\forall</math>, <math>\exists</math>.

#[[quantifier]]s: <math>\forall</math>, <math>\exists</math>.

#parenthesis: <math>(</math>, <math>)</math>.

#parenthesis: <math>(</math>, <math>)</math>.

#The equality symbol <math>=</math>.  

#The [[equality]] symbol <math>=</math>.

 

First-order languages are used to describe [[mathematics]] in [[mathematical notation]] with [[mathematical formula]]e.

[[category:languages]]

[[category:languages]]

[[category:mathematics]]

[[category:mathematics]]