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

Note to entry: ${\displaystyle [\forall a\in A\Rightarrow \max \left(A\right)\ge a]\Rightarrow [\forall b\notin \left[\begin{array}{c}b\notin [\forall a\in A\Rightarrow b\ge a]\Rightarrow [\max \left(a\right)\le b]\end{array}\right]}$ ] Any number is an upper bound of ${\displaystyle \varnothing }$ (empty set) as a set of numbers, because any given number is greater 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 ${\displaystyle \max \left(\varnothing \right)}$ must be smaller than any number; thus ${\displaystyle -\infty }$ .