# Variables and algebraic expressions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

An algebraic expression uses variables, constants, and defined operations to represent a mathematical quantity depending on its inputs.

mko-variable-expression · concept · v0.10.0



## Mathematical statement

The value of an algebraic expression is jointly determined by its variable assignments, scopes, types or number systems, and operation rules. An algebraic expression without an equality sign is not itself an equation.





## Representative formula (exact TeX)

x+1





## Assumptions


- The scope of x and its number system are specified by the context.
- Addition is defined on the type of x, and the constant 1 can be interpreted in that type.





## Symbol scope


- x — variable
- 1 — constant
- + — addition operation





## Intuition, definition, and misconceptions

A variable is a symbol that may take values within an explicit range. The expression x+1 describes a quantity that changes with x; before x is specified, it usually cannot be reduced to one fixed number.

Expressions, equations, and identities play different roles. x+1 is an expression; x+1=3 is an equation requiring two expressions to be equal; an equality holding for every value in a specified domain may be an identity.

Syntactically different expressions may be equivalent in a particular number system, but equivalent rewriting must follow that system’s operation rules rather than visual appearance.

Common mistakes include treating an expression containing a variable as though it already had a fixed value, or treating every text containing x as an equation.





## Adopted derivation guide

[Variables and expressions: a value depends on the assignment, the scope and the number system](https://ocme.evemisslab.com/en/derivations/derivation-mko-variable-expression-01/)The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.





## Prerequisites


- [Arithmetic operations](https://ocme.evemisslab.com/en/mko/mko-arithmetic-operations/) — An algebraic expression combines variables and constants using defined arithmetic operations.





## Verification boundary

This entry does not yet define a general algebraic-expression syntax tree or evaluator and does not claim every rewrite is valid in every number system.

not_formalized

This does not mean the content is false; it means no replayable computational or formal evidence is registered yet.





## Next obligation

Build a minimal typed syntax of variables, constants, and operations with an evaluation function, and verify scope and type boundaries.





## Same-source structured data

This page and the interactive view use the same object and existing language edition; this adds no proof or human review.

[Canonical MKO JSON](https://ocme.evemisslab.com/data/mko/variable-expression.json) · [Plain Markdown](https://ocme.evemisslab.com/en/mko/mko-variable-expression/index.md)