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
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): $\S 16$