# Magma

Magma is a basic kind of algebraic structure, consisting of a set equipped with a single binary operation which must be closed over the set.

A magma is a set `M` matched with an operation, `•`, that sends any two elements `a,b ∈ M` to another element, `a • b ∈ M`.

The symbol, `•`, is a general placeholder for a properly defined operation. To qualify as a magma, the set and operation (M, •) must satisfy the following requirement (known as the magma or closure axiom):

For all $$a, b$$ in $$M$$, the result of the operation $$a \cdot b$$ is also in $$M$$; in mathematical notation:

$$\display{a,b \in M \implies a \cdot b\in M}$$

If $$\cdot$$ is instead a partial operation, then $$S$$ is called a _partial magma_ or more often a _partial groupoid_.
