Definition:Zero (Number)/Naturally Ordered Semigroup

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Definition

Let $\left({S, \circ, \preceq}\right)$ be a naturally ordered semigroup.

Then from axiom $(NO 1)$, $\left({S, \circ, \preceq}\right)$ has a smallest element.


This smallest element of $\left({S, \circ, \preceq}\right)$ is called zero and has the symbol $0$.

That is:

$\forall n \in S: 0 \preceq n$


Also see


Sources