Dividing any number by any random number will surely fetch you an easy result you are looking for but the scenario changes when you try to divide any number by zero or infinity.
Lets try to understand each case.
Any number divided by infinity is zero
First of all, what is infinity ∞? Infinity is a very huge number, a number larger than any assignable or countable number, Right? But can we come up with largest number ever discovered? No, I don't think so. There is always a bigger number than the other.
When we divide number by larger and larger number, the resultant value keeps getting smaller and smaller or we can say that the answer keeps coming closer to zero.
Divide 10 by X and keep increasing value of X
10 / 10 = 1
10 / 100 = .1
10 / 100000 = .0001
10 / 10000000000 = .000000001
10 / 100000000000000000000 = .0000000000000000001
Looking at the above pattern, we see that the answer keeps getting closer to zero as we increase the divisor.
So, for any huge hypothetical number defined as infinity as divisor, we assume that the answer is zero.
Let us understand this by a different logic.
If i ask you to divide 10 by 2, its easy you will say the answer is 5.
But what does it mean.
It means how many times can 2 be deducted from 10.
10 - 2 = 8 (1)
8 - 2 = 6 (2)
6 - 2 = 4 (3)
4 - 2 = 2 (4)
2 - 2 = 0 (5)
That means, if we deduct 2 five times from 10 we get 0.
what happens when we deduct 0 from 10.
Zero can be deducted countless times from 10 and this answer is called infinity.
So, 10 / 0 = ∞
Using above equation,
10 / ∞ = 0.
Any number divided by zero is infinity
Dividing any number by zero would give us infinity or undefined. OK, to make it simpler, if i tell you to handover 10 candies to 5 children in boxes before eating them. Its easy, you will place 2 candies in each box and give it to 5 children and eat the rest candies. If i ask you to give 0 candies to 5 children in boxes and then eat the rest. You can still hand over empty boxes to them and the eat the rest.
0 / 6 = 0
But, what if i tell you to distribute these 10 candies in boxes to 0 children and then eat the rest. Now, there is no way you can do it. You will keep on sitting there till eternity trying to distribute those 10 candies to 0 children and you will never be fortunate enough to let those candies go in your mouth. Empty boxes can be given to children but candies cannot be given to nobody.
Here, candies is divident and children is divisor if you observe.
so 10 / 0 remains undefined or ∞
Mathematically,
Let us consider division of 10 by X where X will keep becoming a smaller and smaller number approaching 0.
10 / 10 = 1
10 / 1 = 10
10 / .0001 = 100,000
10 / .0000000001 = 100,000,000,000
10 / .0000000000000000001 = 100,000,000,000,000,000,000
So, we see that as the divisor is getting smaller and smaller or approaching zero, the answer keeps getting huge and huge.
So,
X / 0 = ∞
Inversely,
X / ∞ = 0
And
0 / 0 = 0
∞ / ∞ = ∞
IVIDING
