extremity vs upper limit

extremity

noun
  • An extreme measure. 

  • The most extreme or furthest point of something. 

  • A hand or foot. 

  • A limb (“major appendage of a human or animal such as an arm, leg, or wing”). 

upper limit

noun
  • The upper limit of a sequence of real numbers is the real number which can be found as follows: remove the first term of the sequence in order to obtain the "first subsequence." Then remove the first term of the first subsequence in order to obtain the "second subsequence." Repeat the removal of first terms in order to obtain a "third subsequence," "fourth subsequence," etc. Find the supremum of each of these subsequences, then find the infimum of all of these supremums. This infimum is the upper limit. 

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