What can actually be divided by zero?
“Dividing by zero…allows you to prove, mathematically, anything in the universe. You can prove that 1+1=42, and from there you can prove that J. Edgar Hoover is a space alien, that William Shakespeare came from Uzbekistan, or even that the sky is polka-dotted.”, Charles Seife, Zero: The Biography of a Dangerous Idea.
As soon as you have seen this question you would have got astonished. What variety of question is this? This question doesn’t make any sense?
It is an issue that we have never encountered in our life because we were taught in class that ‘Never divide by zero’. It rarely makes any sense to divide anything by zero, and if you are attempting to ask Siri to try and do it, she is going to say you have got no friends!
Dividing by zero doesn’t make sense because in arithmetic, dividing by zero may be interpreted as multiplying by zero. 3/0=Y is that the same equation as 0*Y=3. There is not any number that may be plugged for Y to make sure that equation work.
In the search for finding the true meaning of dividing by zero, I came upon a contrasting path. Dividing by zero has two meanings that’s infinity and undefined. I got berserk that how a number can have two meaning. Well, I was able to solve the mystery of infinity and here it goes-:
To understand the concept of infinity we need we’d like to grasp some basic multiplication and division.
For Example-:
3×4 means 3+3+3+3 whereas
4×3 means 4+4+4
3 ×4 means 3+3+3+3 well answer is same thanks to commutative property.
Now understanding the meaning of division
15÷5 means 15–5–5–5 that’s we want to subtract 5 from 15 3 times
Now let’s do the same thing for 1/0
so the question is how many times we want to subtract 0 to get our desired result, lets us understand
1–0–0–0–0–0–0……………. tending to go ∞?
Let’s take another approach-:
1/1=1
1/0.1=10
1/0.01=100
1/0.001=1000
1/0.0001=10000
till we reach to
1/0=∞
Let’s do this for one more time:
2/1=2
2/0.1=20
2/0.01=200
2/0.001=2000
2/0.0001=20000
till we reach to
2/0=∞
So from this discussion, we can conclude that
1/0=∞=2/0
Hence 1=2 (A new discovery!)
We can prove this by the multiplication method also:
1=0⋅∞
= (2⋅0)⋅∞ =2⋅(0⋅∞) = 2⋅1=2
So again 1=2. So from this, we can conclude that concept of infinity is wrong.
So if it doesn’t make any sense we are only left with one undefined option.
So that’s where the true problem is — while zero and infinity are certainly reciprocals of each other, they’re not truly inverses because they don’t multiply to be one. It isn’t division by zero or the introduction of infinity that causes algebra to break, but the way that zero and infinity interact with each other.
As Seife points out, zero may always remain elusive and ineliminable. Zero may stand at the end of time, waiting to be the victor in a universe that it can show will one day die a cold death.
But I can’t even deny the very fact dividing by zero is insane!
While studying the conic section I found a question that was very difficult to be solved.
The question was about finding a point on the curve where the tangent is vertical.
Let’s take an example:
‘Find the point of the curve y³+3x²=12y where tangents are vertical.’
To solve this question I created a secret trick (the magic of dividing by zero) to find the point on the slope of the curve below a specific because sometimes it is difficult to find the slope using algebra. Here it goes:
First, we assumed that vertical means tan90°
So putting dy/dx=1/0 (strange?) ………equation (1)
Then we differentiated the curve-
3y²dy/dx+6x=12dy/dx
3y²dy/dx-12dy/dx=-6x
3dy (y²-4)/dx =-6x
dy/dx=x/4-y²=1/0 ……..From (1)
y²=4
y=±2 these are the points (isn’t it easy)
Well, you might think that isn’t it against the rules to divide by zero, but before you start accusing me of crime remember the quote “Rules are meant to be broken!”.
So lastly we will say that there’s simply no good answer for dividing by zero. The present understanding of mathematical principles starts to interrupt when trying to elucidate dividing by zero although we would have found some application of it (to make questions easy) but to mention we can actually divide it’s not an honest idea. I think diving by zero is more of a theoretical concept than practical and sure at some point this mystery might come to an end (Who knows I might end this mystery).
