Dividing by Zero

By Aditi Madan

In the world of math, many strange results are possible when we try to change it’s rules, but the only rule that most of us have been warned about is “DON’T DIVIDE BY ZERO” 

Have you ever imagined how can a simple number and a basic operation can cause such problems, but before we get to division by zero, let’s figure out what is ‘division’?

For example we have 15/3, what does this mean? 

It means that how many 3s do we require to make a 15?(3+3+3+3+3)

Now we’ll take 77/0, so the question we ask ourselves is how may 0s do we need to add to each other to get 77? There is no answer, we can add 0+0+0….forever but still not get to 77. So it is not defined.

As we know that product of any number and it’s multiplicative inverse is always 1

1) 6*1/6=1

2) 47*1/47=1

If we want to divide by zero, we need to find it’s multiplicative inverse which should be 1/0, this would have to be such a number that multiplying this number by 0 would give 1….1/0*0=1, but we know that anything multiplied by zero is still 0, such a number is impossible, so zero has no multiplicative inverse.

Let’s take another example,

0/20 :This means 20 times what is going to give 0, so if 20(2)=20+20

20(1)=20

20(0)=0  (This shows 0 sets of 20 gives 0)

Now let’s look at the other way 

20/0

This means 0 times what is going to give 20, the answer is undefined as 0 times any number is always 0 and never 20, so it’s undefined.

Zero divide by any number is zero except when 0 is divided by 0 itself(0/0). So again we ask ourselves, how many times do we need to add 0, the answer can be 1,2,5,7,10,1000,1000000……all the answers are correct. In mathematical terms it is indeterminate which means we cannot determine how many times we need to add zero to itself to get to 0. So it can be concluded that anything divided by zero is indeterminate.

Howerver, according to the “Wheel Theory” in mathematics dividing by zero is possible and meaningful and wheel being an algebraic structure, namely a commutative ring and it is an extension to real numbers. It includes division by any real number including zero, And that’s what makes it special.

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Check out our previous post about the derivative of e^x: https://wordpress.com/block-editor/post/mscnm.home.blog/94

Published by mscnm

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