In
mathematics,
division by zero is
division where the divisor (denominator) is
zero. Such a division can be formally
expressed as
a/0 where
a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives
a (assuming
a≠0), and so division by zero is
undefined. Since any number multiplied by zero is zero, the expression 0/0 also has no defined value; when it is the form of a
limit, it is an
indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to
a/0 is contained in
George Berkeley's criticism of
infinitesimal calculus in
The Analyst ("ghosts of departed quantities").