In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as where a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number which, when multiplied by 0, gives a, and so division by zero is undefined. Since any number multiplied by zero is zero, the expression is also undefined; 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 is contained in Anglo-Irish philosopher George Berkeley's criticism of infinitesimal calculus in 1734 in The Analyst.
