Infimum of Subset of Real Numbers/Examples

Examples of Infima of Subsets of Real Numbers

Example 1

The subset $S$ of the real numbers $\R$ defined as:

$S = \set {1, 2, 3}$

admits an infimum:

$\inf S = 1$

Example 2

The subset $T$ of the real numbers $\R$ defined as:

$T = \set {x \in \R: 1 \le x \le 2}$

admits an infimum:

$\inf T = 1$

Example 3

The subset $V$ of the real numbers $\R$ defined as:

$V := \set {x \in \R: x > 0}$

admits an infimum:

$\inf V = 0$