We have studied that 1/0 is equals to infinite , but actually it is not infinite instead it is undefined but why it is not infinite , A famous channel “Numberphile” on youtube answer it nicely in mathematical way but what I will tell is little bit different from what numberphile tells you , you can watch what Numberphile tells you on Youtube and compare it with what i am saying , well both of us gives you same answer but in a different way.
Here I am going to describe it philosophically , philosophy has nice connection with Maths , so let’s dive into philosophy of Maths –
Generally when we ask why 1 divided by zero is infinite then people answer it as below –
The general answer-
First let us understand what is meaning of dividing ? or simply what we mean when we say 4 upon 2 =2 ,it simply means how many times we have to add 2 in order to get 4 , and the simple answer comes out to be 2 , similarly 1/0 means how many number of 0 we need to add in order to get 1 , and the simple answer will be infinite.
Now this above answer is impressive at first sight but actually it has some loopholes , we will criticize above answer which will be helpful to find truth.
Loophole in General answer:-
Let me first define what 0 and 1 are ? what they mean ?
0 simply means nothing
1 simply means something or existence
So 0 means nonexistence
and 1 means existence
Now when someone explain you that adding 0 up to infinite comes out to be 1 has some loopholes , let’s see how ? adding 0 up to infinite looks like this –
Now let me replace this 0 with nothing and 1 with existence
Nothing + nothing + nothing +……………… = Something
Is it possible?
Nothing comes out of Nothing , and Something cannot comes out of Nothing , only Nothing can come out of Nothing.
We can imagine anything in maths but it is not necessary that math always proved practically , the only part of maths which is equivalent to reality , we accept , so nothing can adds up to infinite equals to something does not hold true with reality.
The idea of something out of nothing goes against energy conservation , because energy conservation simply means energy cannot be destroyed which further means something cannot vanishes away into nothingness , so the vice-versa also holds true that nothingness cannot change into something that’s what we mean , energy cannot be created , for scientist,only matter exist , and matter means energy exist , so everything that exist is energy , if some existence came out of nothingness that will obviously contain energy , and energy cannot be created.
So taking 1/0 as infinite is against energy conservation , so it is not infinite , what can we call it as Undefined.