# Formal Mathematical System

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A Formal Mathematical System is a formal system composed of a mathematical language and mathematical operation set to create mathematical arguments.

**AKA:**Theory, Math Formalism, Framework.**Context:**- It can include a set of valid Mathematical Operations.
- It can be an Axiomatic Mathematical Framework.
- It can be analyzed by Theoretical Mathematics.
- It can be represented by a Mathematical Software Program.
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**Example(s):**- an Arithmetic System.
- an Algebraic System.
- a Mathematical Modell.
- an Abstract Rewriting System (ARS), such as string rewriting systems.
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**Counter-Example(s):****See:**Set System, Sigma Algebra.