Infinity or Undefined?

Multiplication is simply repeated addition. For example: 2*4 is simply 2+2+2+2 which equates to 8.

Division, as we’ve all learned in primary school (unless you skipped primary school or you haven’t reached that stage yet), is the opposite of multiplication. So similarly, division is simply repeated subtraction. For example, 8/2 is really 8-2-2-2-2, with the answer equaling the number of 2's removed.

But what about dividing a natural number by zero? (We’ll use 1/0 for this article)

Well the logic presented in the above example doesn’t work. Why though?

Because regardless of how many times we remove zero from 1, it remains the same. So what is the answer? At first glance, one would think the solution is infinity. However, mathematicians have proven that it’s actually undefined. But what’s the difference? Look at the below representation:

1/1=1

1/0.1=10

1/0.01=100

1/0.001=1000

1/0.0001=10000

As the denominator is moving towards zero (decreasing), the answer increases. This implies that 1/0 is infinity.

But hold on. We can also view the denominator as a negative value.

Observe the below representation:

1/-1= -1

1/-0.1= -10

1/-0.01= -100

1/-0.001= -1000

1/-0.0001=-10000

Here, the denominator is increasing towards 0. This, on the other hand, implies that the answer is negative infinity.

The graph above (y=1/x) shows that when x=0 (i.e y=1/0) the answer is virtually positive infinity and negative infinity.

So when we say that 1/0 is undefined, we mean that the solution can be both positive AND negative infinity. Mind=blown.

Chris Francis Anto & Alan Jaison Thanickal