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| '''Division of Zero by Zero''', is an unexplained mystery, since decades in the field of mathematics and is [[indeterminate]]. 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. | | '''Division of Zero by Zero''', is a mathematical concept and is [[indeterminate]]. |
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| == About Zero and it's Operators == | | == Proof of Indeterminacy == |
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| === Discovery === | | We let <math>x=\frac{0}{0}</math>. Rearranging, we get <math>x\cdot0=0</math> there are infinite solutions for this. |
| 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
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| === Operators ===
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| "'''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.
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| == Detailed proof ==
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| We will form two solution sets (namely set(A) and set(B))
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| Solution set(A):
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| If we divide zero by zero then
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| <math>0/0</math>
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| We can write the 0 in the numerator as <math>(1-1) </math> and in the denominator as <math>(1-1)</math>,
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| =<math>(1-1)/(1-1)</math> equaling <math>1</math>
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| We can then write the 0 in the numerator as <math>(2-2) </math> and in the denominator as <math>(1-1)</math>,
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| =<math>(2-2)/(1-1) </math>
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| = <math>2 (1-1)/(1-1) </math> [Taking 2 as common]
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| = <math>2 </math>
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| We can even write the 0 in the numerator as <math>( \infty- \infty) </math> and in the denominator as <math>(1-1)</math>,
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| =<math>( \infty-\infty)/(1-1) </math>
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| = <math> \infty(1-1)/(1-1) </math> [Taking <math> \infty</math> as common]
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| = <math> \infty</math>
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| So, the solution set(A) comprises of all real numbers.
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| set(A) = <math>\{- \infty.....-3,-2,-1,0,1,2,3.... \infty\} </math>
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| Solution set(B):
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| If we divide zero by zero then
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| <math>0/0</math>
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| We know that the actual equation is <math>0^1/0^1 </math>
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| =<math>0^1/0^1 </math>
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| = 0^(1-1) [Laws of Indices, <math>a^m/a^n = a^{m-n} </math>]
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| = <math>0^0 </math>
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| =<math>1 </math> [https://brilliant.org/wiki/what-is-00| Already proven]
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| So, the solution set(B) is a singleton set
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| set(B) =<math>\{1\} </math>
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| Now we can get a finite value to division of <math>0/0 </math> by taking the intersection of both the solution sets.
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| Let the final solution set be <math>F </math>
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| <math>A\bigcap B </math> = <math>F </math>
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| <math>\{- \infty.....-3,-2,-1,0,1,2,3....\infty\} </math> <math>\bigcap </math> <math>\{1\} </math>
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| <math>F </math> = <math>\{1\} </math>
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| Hence proving <math>0/0 =1 </math>
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| {{stub}} | | {{stub}} |
Division of Zero by Zero, is a mathematical concept and is indeterminate.
Proof of Indeterminacy
We let 
. Rearranging, we get 
there are infinite solutions for this.
This article is a stub. Help us out by expanding it.
. Rearranging, we get 
there are infinite solutions for this.
