Etymology
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infra- 
word-forming element meaning "below, beneath," from Latin infra (adverb and preposition) "below, underneath, on the under side, beneath," also "later than; smaller than; inferior to," related to infernus "low, below," from PIE *ndher "under" (source also of Sanskrit adnah "below," Old English under "under, among;" see under). Modern popular use of it dates from the 1920s, as an opposite to super-, often in science fiction. "This use of infra- is scarcely a Latin one" [OED].
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infra (adv.)
"under, below, further on," from Latin infra "below, under, beneath" (see infra-). A Latin word sometimes encountered in footnotes.
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infra-red (adj.)
also infrared, 1873, "below the red" (in the spectrum), from infra- + red (adj.1). As a noun, also from 1873.
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infra dig. 
"beneath one's dignity, unbecoming to one's position in society," 1824, colloquial abbreviation of Latin infra dignitatem "beneath the dignity of." See infra- + dignity.
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infrasonic (adj.)
also infra-sonic, 1920, on the model of supersonic, etc., from infra- + sonic. Or perhaps modeled on French infra-sonore.
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infrastructure (n.)
1887, from French infrastructure (1875); see infra- + structure (n.). The installations that form the basis for any operation or system. Originally in a military sense.
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inferior (adj.)
early 15c., of land, "low, lower down, lower in position," from Latin inferior "lower, farther down" (also used figuratively), comparative of inferus (adj.) "that is below or beneath," from infra "below" (see infra-). Meaning "lower in degree, rank, grade, or importance" is from 1530s; absolutely, "of low quality or rank," also from 1530s.
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fracas (n.)
1727, from French fracas "crash, sudden noise; tumult, bustle, fuss" (15c.), from Italian fracasso "uproar, crash," back-formation from fracassare "to smash, crash, break in pieces," from fra-, a shortening of Latin infra "below" (see infra-) + Italian cassare "to break," from Latin quassare "to shake" (see quash).
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infralapsarian (adj.)

1731, from infra- + Latin lapsus "a fall" (see lapse (n.)) + ending from unitarian, etc.

[In theology], the doctrine held by Augustinians and by many Calvinists, that God planned the creation, permitted the fall, elected a chosen number, planned their redemption, and suffered the remainder to be eternally punished. The Sublapsarians believe that God did not permit but foresaw the fall, while the Supralapsarians hold that God not only permitted but decreed it. [Century Dictionary]
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infernal (adj.)
late 14c., "of or pertaining to the underworld," (ancient Tartarus, the sunless abode of the dead, or the Christian Hell), from Old French enfernal, infernal "of Hell, hellish" (12c.), from Late Latin infernalis "of or belonging to the lower regions," from infernus "hell" (Ambrose), in classical Latin "the lower (world)," noun use of infernus "lower, lying beneath, underground, of the lower regions," from infra "below" (see infra-).

Pluto was infernus rex, and Latin inferi meant "the inhabitants of the infernal regions, the dead." Association of the word with fire and heat is via the Christian conception of Hell. Meaning "devilish, hateful" is from early 15c.; meaning "suitable for or appropriate to Hell" is from c. 1600. As a name of Hell, or a word for things which resemble it, the Italian form inferno has been used in English since 1834, via Dante. Related: Infernally.
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