Is division by zero possible?

Submitted by : SUBHRANIL BANERJEE (Deptartment of BBA (Batch :2017-2020))

It may seem a mind-boggling question. A question may arise in your mind how division by nothing be possible. In mathematics, “division by zero” means a division where the denominator is zero. Some people may say that division of a number by zero gives infinity. Some people may say that division by zero is impossible. 

When you are trying to divide a number by zero in a software. Software may either crash or will show you an error message.              

Don’t get baffled by the question.

Now let’s come to the point,

Look at the graph of f(x) =(1/x)  vs x. It represents a rectangular hyperbola and the curve never cuts y axis (i.e x=0).

For negatives values of x,

f(x) decreases when x increases . For smaller values of x, f(x) decreases gradually with increase in x but rate of decrease of f(x) increases with increase in x and it decreases rapidly when x is very close to zero and going towards negative infinity(-∞).

For positive values of x,

f(x) increases when x decreases .For higher values of x, f(x) increases gradually with decrease in x but rate of increase of f(x) increases with decrease in x and it increases rapidly when x is very close to zero and going towards infinity(∞).

In language of calculus, for existence of a limit, left hand limit and right hand limit must exist and have to be equal.

In this case , we see

So, Left Hand Limit ≠ Right Hand Limit

So, Limit doesn’t exist.

So, Calculus says that division by zero doesn’t make any sense.