What's the difference between i.e. and e.g.?
late 15c., "not endowed with reason" (of beats, etc.); earlier (of quantities) "inexpressible in ordinary numbers" (late 14c.); from Latin irrationalis "without reason," from assimilated form of in- "not, opposite of" (see in- (1)) + rationalis "reason" (see rational). Meaning "illogical, absurd" is attested from 1640s. Related: Irrationally.
irrational ir·ra·tion·al (ĭ-rāsh'ə-nəl)
Not rational; marked by a lack of accord with reason or sound judgment.