equation vs identity

equation

noun
  • The act or process of equating two or more things, or the state of those things being equal (that is, identical). 

  • An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; from which one is to determine a particular quantity. 

  • A small correction to observed values to remove the effects of systematic errors in an observation. 

identity

noun
  • Sameness, identicalness; the quality or fact of (several specified things) being the same. 

  • An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this second element. 

  • A well-known or famous person. 

  • A name or persona—a mask or appearance one presents to the world—by which one is known. 

  • The difference or character that marks off an individual or collective from the rest of the same kind; selfhood; the sense of who something or someone or oneself is, or the recurring characteristics that enable the recognition of such an individual or group by others or themself. 

  • An equation which always holds true regardless of the choice of input variables. 

  • Any function which maps all elements of its domain to themselves. 

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