Well-Ordering Principle

 Let  $ \mathbb{Z}$ denotes set of all integers, that is, $\mathbb{Z} = \{\dots,~ -4,~-3,~-2,~-1,~0,~1,~2,~3,~4,~ \cdots\}$ and $\mathbb{Z}^{+}$ denotes set of all nonnegative integers, that is, $\mathbb{Z}^{+} = \{0,~1,~2,~3,~4,~ \cdots\}$. 


 Well-Ordering Principle: Every nonempty set $S$ of a nonnegative integers contains a least element; that is, there exists integer $a \in S$ such that $a \leq b$ for all $b \in S$.

If we take set $S = \{8,~ 5, ~90, ~3, ~29, ~57\}$. One can observe that $S$ is nonempty and $S \subseteq \mathbb{Z}^{+}$ and $3 \in S$ such that $3$ is less than or equal to all other elements of $S$. So that $3$ is the least element of $S$.




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