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 $$0\cdot x=a,$$ assuming $a\ne 0.$ Rational expressions are also undefined for values that cause division by zero. For example, $$\frac{2x}{5-x}$$ 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.