Smallest Element is Infimum/Examples
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Examples of Use of Smallest Element is Infimum
Example 1
Let $S$ be the subset of the real numbers $\R$ defined as:
- $S = \set {1, 2, 3}$
Then the smallest element of $S$ is $1$.
From Smallest Element is Infimum it follows that:
- $\inf S = 1$
Example 2
Let $T$ be the subset of the set of real numbers $\R$ defined as:
- $T := \set {x \in \R: 1 \le x < 2}$
$T$ has a smallest element $1$.
Hence from Smallest Element is Infimum it follows that $1$ is also the infimum of $T$.