worthlessness has 1 distinct synonym spread across 1 of its 2 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 worth.
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 qualities that would render it valuable or useful
“the drill sergeant's intent was to convince all the recruits of their worthlessness”
Synonyms, antonyms and the broader and narrower relations for worthlessness come from Princeton University’s WordNet. Full sources and licences.
the quality of being without practical use