ISO/TC 211 Multi-Lingual Glossary of Terms (MLGT)

Note to entry: ${\displaystyle [\forall a\in A\Rightarrow \min \left(A\right)\le a]\Rightarrow [\forall b\in \left[\begin{array}{c}b\in [\forall a\in A\Rightarrow b\le a]\Rightarrow \left[\min \left(A\right)\ge b\right]\end{array}\right]}$ Any number is a lower bound of ${\displaystyle \varnothing }$ considered as a set of numbers, because any given number is less than any number in ${\displaystyle \varnothing }$ (an admitted vacuous statement since there is no number in ${\displaystyle \varnothing }$ , but true nonetheless). This means that the ${\displaystyle \min \left(\varnothing \right)}$ must be greater than any number; this ${\displaystyle +\infty }$ .