Cauchy sequence

Spelling & Dictionary Insight

The English entry for Cauchy sequence is 15 letters long, classified as a noun. It sits outside the most-frequent rank tiers, which is often why uncommon words generate more spelling variants per reader. The dominant gloss from Wiktionary reads: "Any sequence x_n in a metric space with metric d such that for every ϵ>0 there exists a natural number N such that for all k,m>N, d(x_k,x_m)<ϵ.".

No misspelling variants are generated for Cauchy sequence in our index, suggesting the orthography follows predictable English patterns. It is not paired with a close-neighbour confusable in our dataset, which tends to mean the word is visually distinctive enough to stand on its own.

Etymologically, the entry records: Named after French mathematician Augustin-Louis Cauchy (1789–1857), who made pioneering contributions to analysis. Root origin matters for spelling because borrowed morphemes (Greek, Latin, Old French, Old English) carry their source-language orthographic conventions into modern English, which is why historical etymology is often the cleanest predictor of whether a cluster like "-ough", "-eau", or "-tion" will appear. For readers arriving here from a spelling check, the authoritative guidance is: the correct English form is Cauchy sequence, spelled C-A-U-C-H-Y- -S-E-Q-U-E-N-C-E, and any other sequence of those letters, regardless of how natural it feels, is a misspelling in standard orthography.