text: In algebra, some arithmetic operations may not assign a meaning to certain values of its operands (e.g., division by zero). In which case, the expressions involving such operands are termed "undefined".
  Undefined terms
  In ancient times, geometers attempted to define every term. For example, Euclid defined a point as "that which has no part". In modern times, mathematicians recognize that attempting to define every word inevitably leads to circular definitions, and therefore leave some terms (such as "point") undefined (see primitive notion for more).
  This more abstract approach allows for fruitful generalizations. In topology, a topological space may be defined as a set of points endowed with certain properties, but in the general setting, the nature of these "points" is left entirely undefined. Likewise, in category theory, a category consists of "objects" and "arrows", which are again primitive, undefined terms. This allows such abstract mathematical theories to be applied to very diverse concrete situations.
  In arithmetic
  The expression  is undefined in arithmetic, as explained in division by zero (the  expression is used in calculus to represent an indeterminate form).
  Mathematicians have different opinions as to whether  should be defined to equal 1, or be left undefined.
  Values for which functions are undefined