Zero (0) is most probably the most mysterious number. The ancient mathematicians were far ahead in Maths but they did not realized about Zero (0). The thought that number how low is it there must have a number. There is no number, how it comes?
The feeling of Zero (0) first came from our subcontinent (Indian subcontinent) and it was a great feel in the field of mathematics. And so we can be proud of our mathematicians.
If any number is multiplied by Zero (0) then the answer is Zero (0). But what if we divide any number by Zero (0)? Is it infinity or undefined?
If you think it is infinity then you are wrong. The answer is undefined. Are you getting confused or thinking that I am wrong, then wait I will prove it to you.
Mathematics if broken when you attempt to divide by zero. Consider the limit of 2/x as x approaches zero.
2/2 = 1
2/1 = 2
2/.5 = 4
2/.1 = 20
2/.01 = 200
2/.0001 = 2000
Now imagine 2/.0000000000000000000000…01. It would be infinitely large. So you might think 2/0 is infinity…
but now approach it from below:
2/(-1) = -2
2/(-.01) = -200
So you might be temped to think it is negative infinity.
Since it cannot be both negative infinity and positive infinity, it is undefined.
Still not satisfied or need more clarification, then wait.
We all know
∞x0 should be equal to A
But we know ∞x0=0
So any thing divided by Zero (0) is undefined.
If we look at everyday life example then it will be clearer to us. Think of you need to divide 100 taka to Zero (0) man, then how much will one get? The answer is undefined. Same is in the case of maths.
Now let’s think another fact. What is 00 (zero to the power zero). Some mathematicians say it is 1 and some say it is 0. Here nothing is need to be said.