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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, when 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 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 *a*/0 is contained in George Berkeley‘s criticism of infinitesimal calculus in 1734 in *The Analyst* (“ghosts of departed quantities”)