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 0a, 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
assuming a=0.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 f(x)=x does not take any values for x less than 0. Note that imaginary numbers allow us to take even roots of negative numbers.