# Division of Zero by Zero

Division of Zero by Zero, is an unexplained mystery, since decades in field of Mathematics and is refereed as undefined. This is been a great mystery to solve for any mathematician and rather to use limits to set value of Zero by Zero in differential calculus one of the Indian-Mathematical-Scientist Jyotiraditya Jadhav has got correct solution set for the process with a proof.

## About Zero and it's Operators

### Discovery

The first recorded zero appeared in Mesopotamia around 3 B.C. The Mayans invented it independently circa 4 A.D. It was later devised in India in the mid-fifth century, spread to Cambodia near the end of the seventh century, and into China and the Islamic countries at the end of the eighth

### Operators

"Zero and its operation are first defined by [Hindu astronomer and mathematician] Brahmagupta in 628," said Gobets. He developed a symbol for zero: a dot underneath numbers.

## Detailed proof

We will form two solution sets (namely set(A) and set(B))

Solution set(A):

If we divide zero by zero then

$0/0$

We can write the 0 in the numerator as $(1-1)$ and in the denominator as $(1-1)$,

=$(1-1)/(1-1)$ equaling $1$

We can then write the 0 in the numerator as $(2-2)$ and in the denominator as $(1-1)$,

=$(2-2)/(1-1)$

= $2 (1-1)/(1-1)$ [Taking 2 as common]

= $2$

We can even write the 0 in the numerator as $( \infty- \infty)$ and in the denominator as $(1-1)$,

=$( \infty-\infty)/(1-1)$

= $\infty(1-1)/(1-1)$ [Taking $\infty$ as common]

= $\infty$

So, the solution set(A) comprises of all real numbers.

set(A) = $\{- \infty.....-3,-2,-1,0,1,2,3.... \infty\}$

Solution set(B):

If we divide zero by zero then

$0/0$

We know that the actual equation is $0^1/0^1$

=$0^1/0^1$

= 0^(1-1) [Laws of Indices, $a^m/a^n = a^{m-n}$]

= $0^0$

=$1$ [Already proven<ref>https://brilliant.org/wiki/what-is-00/</ref>]

So, the solution set(B) is a singleton set

set(B) =$\{1\}$

Now we can get a finite value to division of $0/0$ by taking the intersection of both the solution sets.

Let the final solution set be $F$

$A\bigcap B$ = $F$

$\{- \infty.....-3,-2,-1,0,1,2,3....\infty\}$ $\bigcap$ $\{1\}$

$F$ = $\{1\}$

Hence proving $0/0 =1$