# Division By Zero

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). Whether this expression can be assigned a well-defined value depends upon the mathematical setting. In ordinary (real number) arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 has no defined value and is called 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").

In computer programming, an attempt to divide a floating point number by zero will by default lead to positive or negative infinity by the IEEE 754 floating point standard. However, depending on the programming environment and the type of number (e.g. integer) being divided by zero, it may: generate an exception, generate an error message, cause the program to terminate, generate either positive or negative infinity, or result in a special not-a-number value.

Read more about Division By Zero:  In Elementary Arithmetic, In Algebra, In Higher Mathematics, In Computer Arithmetic

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Division By Zero - In Computer Arithmetic - Historical Accidents
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... The following example uses division by zero to "prove" that 2 = 1, but can be modified to prove that any number equals any other number ... The fallacy is in line 5 the progression from line 4 to line 5 involves division by a − b, which is zero since a equals b ... Since division by zero is undefined, the argument is invalid ...

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