infinite has 13 distinct synonyms spread across 3 of its 5 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is finite.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
having no limits or boundaries in time or space or extent or magnitude
“the infinite ingenuity of man”
(of verbs) not having tense, person, or number (as a participle or gerund or infinitive)
“infinite verb form”
too numerous to be counted
“countless hours”
the unlimited expanse in which everything is located
“they tested his ability to locate objects in space”
1 of the 5 recorded senses carries no synonym, antonym or related term, so it is not shown above. Every sense, with its definition and examples, is on the full entry for infinite.
Synonyms, antonyms and the broader and narrower relations for infinite come from Princeton University’s WordNet. Full sources and licences.