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Undefined Expression
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# Undefined Expression

A mathematical expression is said to be undefined if it is not possible to represent it with the number set being used. A few common examples of undefined expressions are the following.

## Division by Zero

Expressions similar to which show a being divided by 0, are said to be undefined. This is because, there exists no number, x, (real or otherwise) such that
0x=a,
assuming a0. Rational expressions are also undefined for values that cause division by zero. For example,
is undefined when x=5, because the denominator then becomes 0.

## The Root of a Negative Number

Another common example of an undefined expression is the even root of a negative number. Such expressions are not defined when calculating using real numbers. This means that the function does not take any values for x less than 0. Note that imaginary numbers allow us to take even roots of negative numbers.
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