Webster's English Dictionary

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irrational

1. ir.ra.tio.nal \(')ir-'(r)ash-n*l, -*n-*l\ \(.)ir-.(r)ash-*-'nal-*t-e-\ 
   \(')ir-'(r)ash-n*-le-, -*n-*l-e-\ aj [ME, fr. L irrationalis, fr. in- + 
   rationalis rational] : not rational : as  : not endowed with reason or 
   understanding  : lacking usual or normal mental clarity or coherence  : not 
   governed by or according to reason {~ fears}  in ancient prosody  of a 
   syllable  : having a quantity other than that required by the meter  of a 
   foot  : containing such a syllable reason. IRRATIONAL may imply actual 
   mental derangement but more often suggests words or actions directly in 
   conflict with reason {irrational beliefs} UNREASONABLE suggests guidance by 
   some force other than reason (as self-will, rage) that makes one deficient 
   in good sense {unreasonable extravagance} - ir.ra.tio.nal.i.ty n SYN syn 
   IRRATIONAL, UNREASONABLE mean not governed or guided by 
2. irrational n 1: an irrational being  2: a real number that is not 
   expressible as the quotient of two integers