Why can't we divide by 0?

Why can't we divide by 0?

Image credit: istockphoto.com

  Rules are made to be broken. But unfortunately, in the world of mathematics, it's not possible. If we do that we get strange results. But there's still one thing that we can't do even after breaking rules- dividing by 0...

Why can't we divide by 0?

  Zero, a very basic number that we study since our kindergarten. And division, a very basic operation. How can the combination of such simple and basic number and operation can cause a big problem?

  As you divide a number by smaller and smaller numbers, the answers become bigger and bigger.

For example:

2÷2=1

2÷1=2

2÷0.5=4

2÷0.25=8

2÷0.001=2000

2÷0.0000000001=20000000000

And the smaller the number, you will get bigger and more bigger answers. This means that if we divide a number by 0, the answer should be ∞. But it's not infinity. Why?

Why can't 1/0 be ∞?

  To understand why, let's have a closer look at division. If I say 20÷2, it means I have to count that how many time I add 2 to get twenty, i.e., 2+2+2+2+2+2+2+2+2+2=20. Therefore, 20÷2 is 10. It also means that 10×2=20. 

  Now, if 5×2=10 we can say that 10×1/2=5. Here, 2 and 1/2 are called as multiplicative inverse. But 2×1/2=1. Thus the multiplication of a number and the multiplicative inverse of it is 1. Then for 0, its multiplicative inverse might be 1/0. But when we multiply 0 and its multiplicative inverse, we don't get 1, we get 0. 0×1/0=0. This is because anything multiplied with 0 is 0.

  Mathematicians have broken and created a lot of rules that worked out. But then why can't mathematicians consider 1/0 as ∞. Let's say it's considered. Then,

0×∞=1...as now ∞ is the multiplicative inverse of 0.

This means that,

(0×∞)+(0×∞) should be 2.

But,

(0×∞)+(0×∞)=(0+0)×(∞)=0×∞=2

But 0×∞=1 and 0×∞=2???

This means 1=2.

It is not wrong but certainly not possible in our today's mathematical world. But this at least proves that we can't consider 1/0 as ∞.

  For mathematical minds, this post might be like a snap of fingers. But there are people wondering what the hell 0 did in its last birth that we can't divide anything by it today...

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I thought it would be better not to delete or revamp these posts, even if they suck. The bitter truth is that old works always suck, but I take that as a positive tool to convey that I am growing. Besides there's no better way to showcase my journey without these old, messy, poorly written posts!

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