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