invalid vs irrational

invalid

adj
  • Not valid; not true, correct, acceptable or appropriate. 

  • Suffering from disability or illness. 

  • Intended for use by an invalid. 

verb
  • To make invalid or affect with disease. 

  • To exempt from (often military) duty because of injury or ill health. 

irrational

adj
  • Not rational; unfounded or nonsensical. 

  • Of a real number, that cannot be written as the ratio of two integers. 

noun
  • A real number that can not be expressed as the quotient of two integers, an irrational number. 

How often have the words invalid and irrational occurred in a corpus of books? (source: Google Ngram Viewer )