invalid vs rational

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. 

rational

adj
  • Logically sound; not self-contradictory or otherwise absurd. 

  • Healthy or balanced intellectually; exhibiting reasonableness. 

  • Of an algebraic expression, capable of being expressed as the ratio of two polynomials. 

  • Expressing the type, structure, relations, and reactions of a compound; graphic; said of formulae. 

  • Of a number, capable of being expressed as the ratio of two integers. 

  • Expressing a physical object. 

  • Capable of reasoning. 

noun
  • A rational number: a number that can be expressed as the quotient of two integers. 

  • The breastplate worn by Israelite high priests. 

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