Etymology
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infant (n.)
Origin and meaning of infant
late 14c., infant, infaunt, "a child," also especially "child during earliest period of life, a newborn" (sometimes meaning a fetus), from Latin infantem (nominative infans) "young child, babe in arms," noun use of adjective meaning "not able to speak," from in- "not, opposite of" (see in- (1)) + fans, present participle of fari "to speak," from PIE root *bha- (2) "to speak, tell, say." As an adjective in English, 1580s, from the noun.

The Romans extended the sense of Latin infans to include older children, hence French enfant "child," Italian fanciullo, fanciulla. In English the word formerly also had the wider sense of "child" (commonly reckoned as up to age 7). The common Germanic words for "child" (represented in English by bairn and child) also are sense extensions of words that originally must have meant "newborn."
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infantile (adj.)
mid-15c., "pertaining to infants," from Late Latin infantilis "pertaining to an infant," from infans "young child" (see infant). Sense of "infant-like" is from 1772.
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Infanta (n.)
"daughter of a king of Spain or Portugal," c. 1600, from Spanish and Portuguese infanta, fem. of infante "a youth; a prince of royal blood," from Latin infantem (see infant).
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enfant terrible (n.)
1851, French, literally "terrible child" (see infant + terrible). One whose unorthodox or shocking speech or manners embarrass his associates as a naughty child embarrasses his elders. French also has enfant gâté, "spoiled child," hence "person given excessive adulation."
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infantry (n.)
Origin and meaning of infantry
1570s, from French infantrie, infanterie (16c.), from older Italian or Spanish infanteria "foot soldiers, force composed of those too inexperienced or low in rank to be cavalry," a collective noun from infante "foot soldier," originally "a youth," from Latin infantem (see infant). Meaning "infants collectively" is recorded from 1610s. A Middle English (c. 1200) word for "foot-soldiers" was going-folc, literally "going-folk."
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infanticide (n.)

1650s, "the killing of infants," especially the killing of newborns or the unborn; 1670s, "one who kills an infant," from infant + -cide. Perhaps from French infanticide (16c.).

In Christian and Hebrew communities infanticide has always been regarded as not less criminal than any other kind of murder; but in most others, in both ancient and modern times, it has been practised and regarded as even excusable, and in some enjoined and legally performed, as in cases of congenital weakness or deformity among some of the communities of ancient Greece. [Century Dictionary]
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Fauntleroy 
in various usages, from the gentle boy hero of Frances Hodgson Burnett's popular novel "Little Lord Fauntleroy" (1885). The family name is recorded from mid-13c., literally "son of the king" (Anglo-French Le Enfant le Roy), from faunt, a Middle English variant of enfaunt (see infant). Middle English also had fauntekin "a little child" (late 14c.).
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infancy (n.)
late 14c., "condition of babyhood," also "childhood, youth," from Anglo-French enfaunce and directly from Latin infantia "early childhood," from infantem "young child," literally "one unable to speak" (see infant). Restriction to the earliest months of life is a return to the etymological sense of the word but is a recent development in English. In old legal language it meant "condition of being a minor" and could mean any age up to 21.
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*bha- (2)

*bhā-; Proto-Indo-European root meaning "to speak, tell, say."

It forms all or part of: abandon; affable; anthem; antiphon; aphasia; aphonia; aphonic; apophasis; apophatic; ban (n.1) "proclamation or edict;" ban (v.); banal; bandit; banish; banlieue; banns (n.); bifarious; blame; blaspheme; blasphemy; boon (n.); cacophony; confess; contraband; defame; dysphemism; euphemism; euphony; fable; fabulous; fado; fairy; fame; famous; fandango; fatal; fate; fateful; fatuous; fay; gramophone; heterophemy; homophone; ineffable; infamous; infamy; infant; infantile; infantry; mauvais; megaphone; microphone; monophonic; nefandous; nefarious; phatic; -phone; phone (n.2) "elementary sound of a spoken language;" phoneme; phonetic; phonic; phonics; phono-; pheme; -phemia; Polyphemus; polyphony; preface; profess; profession; professional; professor; prophecy; prophet; prophetic; quadraphonic; symphony; telephone; xylophone.

It is the hypothetical source of/evidence for its existence is provided by: Greek pheme "speech, voice, utterance, a speaking, talk," phōnē "voice, sound" of a human or animal, also "tone, voice, pronunciation, speech," phanai "to speak;" Sanskrit bhanati "speaks;" Latin fari "to say," fabula "narrative, account, tale, story," fama "talk, rumor, report; reputation, public opinion; renown, reputation;" Armenian ban, bay "word, term;" Old Church Slavonic bajati "to talk, tell;" Old English boian "to boast," ben "prayer, request;" Old Irish bann "law."

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SIDS (n.)
1970, acronym for Sudden Infant Death Syndrome.
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