Smallest Element is Infimum/Examples

Examples of Use of Smallest Element is Infimum

Arbitrary 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:

$\inf S = 1$


Arbitrary 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 $T$.

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