Given a set S and an operation
+, we say that
(S, +) is a semigroup if it satisfies the following properties for any x, y, z ∈ S:
x + y∈ S
(x + y) + z = x + (y + z)
We also say that S forms a semigroup under +.
Examples of Semigroups
- Strings form a semigroup under concatenation.
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