Etymology
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REM (n.1)

also R.E.M., rem, unit for measuring ionizing radiation, 1947, acronym of roentgen equivalent man.

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sleep (n.)

Old English slæp "sleep, sleepiness, inactivity," from Proto-Germanic *slepaz, from the root of sleep (v.); compare cognate Old Saxon slap, Old Frisian slep, Middle Dutch slæp, Dutch slaap, Old High German slaf, German Schlaf, Gothic sleps.

Personified in English from late 14c., on model of Latin Somnus, Greek Hypnos. Figurative use for "repose of death" was in Old English; to put (an animal) to sleep "kill painlessly" is recorded from 1923 (a similar imagery is in cemetery). Sleep deprivation attested from 1906. Sleep-walker "somnambulist" is attested from 1747; sleep-walking is from 1840. To be able to do something in (one's) sleep "easily" is recorded from 1953. Sleep apnea is by 1916.

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REM (n.2)

also R.E.M., rem, 1957, initialism (acronym) for rapid eye movement.

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sleep (v.)

Old English slæpan "to be or fall asleep; be dormant or inactive" (class VII strong verb; past tense slep, past participle slæpen), from Proto-Germanic *slēpanan (source also of Old Saxon slapan, Old Frisian slepa, Middle Dutch slapen, Dutch slapen, Old High German slafen, German schlafen, Gothic slepan "to sleep"), from PIE *sleb- "to be weak, sleep," which perhaps is connected to PIE root *sleg- "be slack, be languid," the source of slack (adj.). Sleep with "do the sex act with" is in Old English:

Gif hwa fæmnan beswice unbeweddode, and hire mid slæpe ... [Laws of King Alfred, c. 900]

Related: Slept; sleeping. Sleep around is attested by 1928.

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sleep-over (n.)
1935, from verbal phrase; see sleep (v.) + over (adv.).
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hypnotic (adj.)
1620s, of drugs, "inducing sleep," from French hypnotique (16c.) "inclined to sleep, soporific," from Late Latin hypnoticus, from Greek hypnotikos "inclined to sleep, putting to sleep, sleepy," from hypnoun "put to sleep," from hypnos "sleep" (from PIE root *swep- "to sleep"). Modern sense of "pertaining to an induced trance" first recorded in English 1843, along with hypnotize, hypnotism, hypnotist, in the works of hypnotism pioneer Dr. James Braid. Related: Hypnotical; hypnotically.
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hypno- 
word-forming element meaning "sleep," from Greek hypnos "sleep," from PIE *supno-, suffixed form of root *swep- "to sleep."
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insomnia (n.)
"chronic inability to sleep," 1620s, insomnie, from Latin insomnia "want of sleep, sleeplessness," from insomnis "sleepless," from in- "not" (see in- (1)) + somnus "sleep" (from PIE root *swep- "to sleep"). The re-Latinized form is from 1758.
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somni- 
before vowels somn-, word-forming element meaning "sleep," from combining form of Latin somnus "sleep, slumber," from PIE root *swep- "to sleep."
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Somnus (n.)
"sleep personified; the god of sleep in Roman mythology," equivalent of Greek Hypnos, son of Night and brother of Death, 1590s, from Latin somnus "sleep, drowsiness," from PIE *swep-no-, suffixed form of root *swep- "to sleep."
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