Question

What is the value of 0/0?

Answer 1

Answer:

The value of 0/0 is indeterminate form and there are other number that are indeterminate forms.

Explanation:

Numbers of Inderminate Form:

Indeterminate Form is a form of a number whose limit is not defined till today and whose value is neither .

Mathematicians have not been able to identify the limit of these numbers.

There are mainly seven indeterminate forms present till today:

$1) \: \frac{0}{0}$

$2) \: \frac{ \infty }{ \infty }$

$3) \: 0 \times \infty$

$4) \: \infty - \infty$

$5) \: {0}^{0}$

$6) \: {1}^{ \infty }$

$7) \: { \infty }^{0}$

These above seven forms are indeterminate forms.

These indeterminate forms always come due to some calculation that bring the answer to zero/zero.

So, to avoid this in calculus we approach the problem in another way so as to avoid the resultant to be zero/zero.

Answer 2

Consider you have some chocolates in a plate. There is one long queue is waiting for you to get the chocolates. You’re not going to show the plate to them, so nobody knows how many chocolates you have.

You have 6 chocolates in the plate. You decided to give 2 chocolates to each of them. You can satisfy 3 people. 6/2 = 3.

Now you want to cheat them. You're just pretending that you are giving them chocolates. You have 6; you can satisfy an infinite number of people( Hopefully, they won’t get irritated by the fact that you’re fooling them.) 6/0=infinity.

If you don’t have any chocolates in your plates how many numbers of people will be satisfied? Zero! 0/2 = 0. (If you're acting so generous, you can’t satisfy anybody!)

Now comes tricky one! You are having nothing, but trying to act smartly. You are going to do point no 2 here. Yes, you pretend! You are having nothing and giving nothing. How many people will be satisfied? The answer is undefined, indeterminate form! Why? Anyone can find that you are cheating him by simply asking you to show the plate. You have been caught. Anybody in the queue can find this. It can be the first person, 2nd person or Nth person. How many people have you satisfied? Answer is N-1 people. Now you have to bare with this insane indeterminate!

Mathematically speaking, you can’t say zero as it is exactly zero. Zero can be anything which approaches zero. Consider a tiny number called 0.00000…1, you don’t know the exact value of this. You simply said zero.

Now you are going to divide one zero with another zero. (You can’t say both are same; they can be anything tiny, immeasurable number!) The answer can be any positive value or zero. Better to say as undefined.