Division of Zero by Zero

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Now if we divide Zero by Zero the equation looks like: 0/0 but it is currently undefined,

If we now try to prove it then.

The summing method

If we take 0/0 then we can also write it as (1-1)/(1-1) then it equals to 1, now if we take the 0 in numerator as (2-2) and other zero in denominator as (1-1) then it also equates to 2.

{(2-2)/(1-1)= 2(1-1)/(1-1) = 2} , now if we write it as {(\(\infty - \infty\))/(1-1) then it equates to \(\infty\)}

so, we can conclude that division of 0/0 can equate to any value of integers till infinity.

Using laws of Indices

Now if we use laws of Indices, then,

\(0/0 = 0^1/0^1\) = 0^1-1 (As, a^m/a^n = a^m-n)

then 0^0 = 1 which is already proven,

so 0/0 should also equate to 1 only in this case.

Conclusion

Now, we used two methods to find actual value of 0/0 and the common answer to both of them is 1, so we can conclude that the division of 0/0 equated to 1.

Acknowledgment

This proof is done by Jyotiraditya Jadhav