The less-than relation is irreflexive on the integers.
British Dictionary definitions for irreflexive
irreflexive
/ˌɪrɪˈflɛksɪv/
adjective
1.
(logic) (of a relation) failing to hold between each member of its domain and itself: `… is distinct from …' is irreflexive Compare reflexive (sense 4), nonreflexive