eng

### maximum <mathematics>

### least upper bound <mathematics>

max <mathematics>

smallest element larger than or equal to all elements of a set contained in an ordered domain <<math>>

Note to entry: \[[\forall a \in A \implies max(A) \geq a] \implies [\forall b \ni [(b \ni [\forall a \in A \implies b \geq a] \implies [max(a) \leq b]]\] Any number is an upper bound of `O/` (empty set) as a set of numbers, because any given number is greater than any number in `O/` (an admitted vacuous statement since there is no number in `O/`, but true nonetheless). This means that the `max(O/)` must be smaller than any number; thus `-oo`.

ORIGIN: ISO/TC 211 Glossary of Terms - English (last updated: 2020-06-02)