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.
Expressions similar to which show being divided by are said to be undefined. This is because, there exists no number, (real or otherwise) such that assuming Rational expressions are also undefined for values that cause division by zero. For example, is undefined when , because the denominator then becomes
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 less than Note that imaginary numbers allow us to take even roots of negative numbers.