---
tag: 6D3WA7N2W4
kind: concept
name: Term
msc: [03B10, 03C07]
sources:
  - url: https://en.wikipedia.org/wiki/Term_(logic)
same_as:
  wikidata: Q1318370
  wikipedia: Term (logic)
---

## Summary

A term is an expression of a first-order language that names an object.
Terms are built from variables and constant symbols by applying function symbols of the [[signature|WDVVEYD6AT]].
In a [[structure|983GZBQYT4]], once the variables have values, each term has a value, which is an element of the structure.
Terms play the role of nouns in logic, while formulas play the role of statements.

## Explanations

### L1 human

In the language of arithmetic, $x + 1$ and $(x \cdot y) + 0$ are terms.
They stand for numbers once you say what $x$ and $y$ are.
For example, with $x = 3$ the term $x + 1$ has value $4$.
An expression such as $x < y$ is not a term: it does not name a number but makes a claim.