maximal vs minimum

maximal

noun
  • The element of a set with the greatest magnitude. 

  • Said of a set of well-formed formulas: that it is as large as it can be without being inconsistent; i.e. that for any well-formed formula φ, the set contains either φ or ~φ. 

  • Said of an ideal of a ring or a filter of a lattice: that it is as large as it can be without being trivial (improper). 

adj
  • Largest, greatest (in magnitude), highest, most. 

minimum

noun
  • A lower bound of a set which is also an element of that set. 

  • The smallest amount. 

  • He always tries to get away with doing the minimum. 

  • The lowest limit. 

  • A period of minimum brightness or energy intensity (of a star). 

  • The smallest member of a batch or sample or the lower bound of a probability distribution. 

adj
  • To the lowest degree. 

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