Etymology
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Words related to infer

*en 
Proto-Indo-European root meaning "in."

It forms all or part of: and; atoll; dysentery; embargo; embarrass; embryo; empire; employ; en- (1) "in; into;" en- (2) "near, at, in, on, within;" enclave; endo-; enema; engine; enoptomancy; enter; enteric; enteritis; entero-; entice; ento-; entrails; envoy; envy; episode; esoteric; imbroglio; immolate; immure; impede; impend; impetus; important; impostor; impresario; impromptu; in; in- (2) "into, in, on, upon;" inchoate; incite; increase; inculcate; incumbent; industry; indigence; inflict; ingenuous; ingest; inly; inmost; inn; innate; inner; innuendo; inoculate; insignia; instant; intaglio; inter-; interim; interior; intern; internal; intestine; intimate (adj.) "closely acquainted, very familiar;" intra-; intricate; intrinsic; intro-; introduce; introduction; introit; introspect; invert; mesentery.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit antara- "interior;" Greek en "in," eis "into," endon "within;" Latin in "in, into," intro "inward," intra "inside, within;" Old Irish in, Welsh yn, Old Church Slavonic on-, Old English in "in, into," inne "within, inside."
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*bher- (1)

Proto-Indo-European root meaning "to carry," also "to bear children."

It forms all or part of: Aberdeen; amphora; anaphora; aquifer; auriferous; bairn; barrow (n.1) "frame for carrying a load;" bear (v.); bearing; Berenice; bier; birth; bring; burden (n.1) "a load;" carboniferous; Christopher; chromatophore; circumference; confer; conference; conifer; cumber; cumbersome; defer (v.2) "yield;" differ; difference; differentiate; efferent; esophagus; euphoria; ferret; fertile; Foraminifera; forbear (v.); fossiliferous; furtive; indifferent; infer; Inverness; Lucifer; metaphor; odoriferous; offer; opprobrium; overbear; paraphernalia; periphery; pestiferous; pheromone; phoresy; phosphorus; Porifera; prefer; proffer; proliferation; pyrophoric; refer; reference; semaphore; somniferous; splendiferous; suffer; transfer; vociferate; vociferous.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit bharati "he carries, brings," bhrtih "a bringing, maintenance;" Avestan baraiti "carries;" Old Persian barantiy "they carry;" Armenian berem "I carry;" Greek pherein "to carry," pherne "dowry;" Latin ferre "to bear, carry," fors (genitive fortis) "chance, luck," perhaps fur "a thief;" Old Irish beru/berim "I catch, I bring forth," beirid "to carry;" Old Welsh beryt "to flow;" Gothic bairan "to carry;" Old English and Old High German beran, Old Norse bera "barrow;" Old Church Slavonic birati "to take;" Russian brat' "to take," bremya "a burden," beremennaya "pregnant."

illative (adj.)
1610s, "stating or introducing an inference" (of words such as because, then, therefore); 1630s, "inferential, arising from inference," from Late Latin illativus, from Latin illatus "brought in," used as past participle of inferre "to bring in, introduce" (see infer). Grammatical sense "case expressing motion into" is from 1890. As a noun from 1590s, "illative word." Related: Illation "action of inferring" (1530s).
imply (v.)
late 14c., implien, emplien "to enfold, enwrap, entangle" (the classical Latin sense), from Old French emplier, from Latin implicare "involve, enfold, entangle," from assimilated form of in- "into, in, on, upon" (from PIE root *en "in") + plicare "to fold" (from PIE root *plek- "to plait").

Meaning "to involve something unstated as a logical consequence" first recorded c. 1400; that of "to hint at" is from 1580s. Related: Implied; implying. The distinction between imply and infer is in "What do you imply by that remark?" but, "What am I to infer from that remark?" Or, as Century Dictionary puts it, "An action implies ability or preparation, but involves consequences."
inference (n.)
1590s, "action of inferring;" 1610s, "that which is inferred;" from Medieval Latin inferentia, from Latin inferentem (nominative inferens), present participle of inferre "bring into; conclude, deduce" (see infer).