section_path: History
section_name: History
paragraph_text: History
  
  The concept of a set emerged in mathematics at the end of the 19th century. The German word for set, Menge, was coined by Bernard Bolzano in his work Paradoxes of the Infinite.
  
  Georg Cantor, one of the founders of set theory, gave the following definition at the beginning of his Beiträge zur Begründung der transfiniten Mengenlehre:
  
  A set is a gathering together into a whole of definite, distinct objects of our perception or our thought—which are called elements of the set.
  
  Bertrand Russell introduced the distinction between a set and a class (a set is a class, but some classes, such as the class of all sets, are not sets; see Russell's paradox):
  
  When mathematicians deal with what they call a manifold, aggregate, Menge, ensemble, or some equivalent name, it is common, especially where the number of terms involved is finite, to regard the object in question (which is in fact a class) as defined by the enumeration of its terms, and as consisting possibly of a single term, which in that case is the class.