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What does undefined mean in math?

August 3, 2022
written by Azhar Ejaz

I believe that every student faces this question at least once in their academic career.

Students often struggle to understand the concept of undefined. But why do students struggle with undefined? It might be due to the fact that they are not able to define the term.

The term undefined is used when you can’t tell the difference between a number and a real number.

The concept of undefined is a fundamental part of mathematics. You can’t learn any topic in math without understanding it.

Here is how you can learn what undefined means in math.

 What is undefined?

The term undefined means that you don’t have a clear answer. You are unable to tell the difference between real numbers and numbers. In mathematics,

undefined means a term that is mathematically inexpressible, or doesn’t have a clear answer. Anything divided by zero is considered undefined by the rules of mathematics. Take a fraction such a

8/2=x –->1

 Multiply by 2 both side equation (1) we get,



Only possible value for x is4

 But doing the same for 5/0=x multiplying both sides by zero produces 5=0.x which is impossible and,



If the denominator is equal to zero a (3/0=undefined)

if any expression in math denominator is equal to zero =undefined

[Infinity, k/ 0]–> undefined.

The concept of undefined is used in various topics of math like calculus, trigonometry, linear algebra, etc.

In calculus, you can’t differentiate functions that have undefined.

In trigonometry, you can’t tell the difference between the sin of an undefined and an actual number.

In linear algebra, you can’t find the determinant of matrices that have undefined.

Practice Problems that Have Undefined

It is quite difficult to solve problems that have been undefined. However, you can practice with problems that are not exactly like the problem you will encounter.