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Why is any number over 0 undefined or what we say infinity?

 

Why is any number over 0 undefined or what we say infinity?

We are used to dividing a certain number by another or by the same number since we started learning mathematics. That’s not a big deal. But here’s one big deal that we are always warned about i.e., to divide any number by zero (0).  But Why? Because you get infinity when you do so. But how and why we tend to get so when we divide any number by zero?

Let’s have a look at it to better understand!!!

▪         Firstly, what’s multiplication? Nothing but repeated addition.

Example: 2×3=6 which means we need to add 2 thrice to get 6.            

▪         And secondly, what’s division? Nothing but repeated subtraction unless we get zero.

Example: 15/5=3 which means subtracting 5 thrice from 15 to get 0.  i.e, 15-5-5-5=0

But let’s check in case of 1/0. According to the above shown theory of division, we need to find the amount of times we need to subtract 0 from 1.

i.e.,1/0=1-0-0-0-0-0-0-.................

Uh Oh,it looks like this will keep going on forever (infinite times) but still we won't know how much 0's are required to be subtracted from 1 for the result to be 0. So simply, we cannot define 1/0 in normal division terms and hence is undefined.

In other words,here we are not able to find the limit of the zero that should be subtracted. So, 1/0 can be considered undefined.

Clear now??? If not, let’s have a look at another approach.

Let’s do simple division of same number by decreasing the values of denominator!!!

1/1=1,     1/0.1=10,     1/0.01=100,     1/0.001=1000,     1/0.0001=10000 Here, the value of the expression goes on increasing when we decrease the value of denominator. So, when the value of denominator tends to or equals to zero, then the value of the expression tends to or becomes so large that we cannot find it's bound or in others it becomes infinity i.e., 1/0=∞.

Clear and simple! Yes? But wait, there’s one big problem in this. Now, what’s that?

Here, we did the division procedure for only one number ‘1’. Let’s check for ‘2’.

2/1=2,   2/0.1=20,    2/0.01=200,    2/0.001=2000,   2/0.0001=20000 Same as previous, the value goes on increasing. And on dividing 2 by 0, we get infinity i.e., 2/0=∞

Doesn’t it seem like a bit unconvincing that 1 over 0 and 2 over 0 both are equal to infinity (∞)?

So, from the above results, 1/0=2/0 and from the basic mathematics rule we can write 1=2 which is mathematically and logically incorrect. 1≠2.

Thus, it becomes more complicated and finally here we conclude that any number when divided by zero is undefined.


- kashish Mahato

 

 

 

 

 

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