How alike are two texts by the WORDS they use? Jaccard similarity is dead simple: the size of the shared vocabulary divided by the size of the combined vocabulary. Identical word-sets give 1, no overlap gives 0. It’s the workhorse behind plagiarism checks, deduplication, and ‘related documents’. Slide the two passages together and watch the overlap grow.
Jaccard similarity J(A,B) = |A ∩ B| / |A ∪ B|: the intersection of two sets over their union, in [0,1]. For text it’s computed on word (or shingle) sets — 1 means identical vocabularies, 0 means disjoint. Cheap and interpretable, it underlies near-duplicate detection and MinHash/LSH at scale. A fail-loud self-check throws unless identical sets give J=1 and disjoint sets give J=0. ◆ real set theory, node-verified.
The two word-sets are interpolated for the demo; the intersection-over-union is exact. Jaccard sees VOCABULARY overlap only — it ignores order, grammar, and meaning; two texts can share words yet say opposite things.