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{{ printedBook.courseTrack.name }} {{ printedBook.name }} 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 $0a ,$ 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 $0⋅x=a,$ assuming $a =0.$ Rational expressions are also undefined for values that cause division by zero. For example, $5−x2x $ 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)=x $ does not take any values for $x$ less than $0.$ Note that imaginary numbers allow us to take even roots of negative numbers.