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Random information on the term “undefined”:
In mathematics, undefined has several different meanings, depending on the context. Such contexts include the following, among others:
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, “point” for example, undefined (see primitive notion).
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”; again, these are primitive, undefined terms. This allows such abstract mathematical theories to be applied to very diverse concrete situations.
The expression 0/0 is undefined in arithmetic, as explained in division by zero (the expression is used in calculus to represent an indeterminate form).