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Origin and history of irrational

irrational(adj.)

late 15c., "not endowed with reason" (of beasts, etc.), from Latin irrationalis/inrationalis "without reason, not rational," from assimilated form of in- "not, opposite of" (see in- (1)) + rationalis "of or belonging to reason, reasonable" (see rational (adj.)).

Meaning "illogical, absurd" is attested from 1640s. Related: Irrationally. The mathematical sense "inexpressible in ordinary numbers" is from late 14c. in English, from use of the Latin word as a translation of Greek alogon in Euclid.

Entries linking to irrational

late 14c., racional, "pertaining to or springing from reason;" mid-15c., of persons, "endowed with reason, having the power of reasoning," from Old French racionel and directly from Latin rationalis "of or belonging to reason, reasonable," from ratio (genitive rationis) "reckoning, calculation, reason" (see ratio).

In arithmetic, "expressible in finite terms," 1560s. Meaning "conformable to the precepts of practical reason" is from 1630s. Related: Rationally. It is from the same source as ratio and ration; the sense in rational is aligned with that in related reason (n.), which got deformed in French.

1560s, originally in the mathematical sense, from irrational + -ity. Meaning "unreasonableness, absurdity" is from 1640s.

word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."

In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.

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