Difference between revisions of "Division of Zero by Zero"

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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 '''[https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwij6oLv_OvwAhVT83MBHc1LCzQQFjAHegQIDhAD&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FDifferential_calculus%23%3A~%3Atext%3DIn%2520mathematics%252C%2520differential%2520calculus%2520is%2Cthe%2520area%2520beneath%2520a%2520curve.&usg=AOvVaw1YROgVEzpqoR0TXuAWa-Ju differential calculus]''' one of the Indian-Mathematical-Scientist '''[[Jyotiraditya Jadhav]]''' has got correct solution set for the process with a proof.  
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'''Division of Zero by Zero''', is a mathematical concept and is [[indeterminate]].
  
== About Zero and it's Operators ==
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== Proof of Indeterminacy ==
  
=== Discovery ===
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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
 
  
=== 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 ==
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We will form two solution sets namely set(A) and set(B)
 
 
 
 
 
Solution set(A):
 
 
 
Now if we divide zero by zero then
 
 
 
<math>0/0</math>
 
 
 
we can write the 0 in the numerator as <math>(1-1) </math> and again other in the denominator as <math>(1-1)</math>,
 
 
 
 
 
=<math>(1-1)/(1-1)</math> and that equals to be <math>1</math>
 
 
 
 
 
Now we can write the 0 in the numerator as <math>(2-2) </math> and again other in the denominator as <math>(1-1)</math>,
 
 
 
 
 
=<math>(2-2)/(1-1)  </math>
 
 
 
= <math>2 (1-1)/(1-1) </math>                                                              [Taking 2 as common]
 
 
 
= <math>2 </math>
 
 
 
 
 
Now we can write the 0 in the numerator as <math>( \infty- \infty) </math> and again other in the denominator as <math>(1-1)</math>,
 
 
 
 
 
=<math>( \infty-\infty)/(1-1) </math>
 
 
 
= <math> \infty(1-1)/(1-1) </math>                                                            [Taking <math> \infty</math> as common]
 
 
 
= <math> \infty</math>
 
 
 
 
 
So, the solution set(A) comprises of all the values of real numbers.
 
 
 
 
 
set(A) = <math>\{- \infty.....-3,-2,-1,0,1,2,3.... \infty\}  </math>
 
 
 
 
 
Solution set(B):
 
 
 
Now if we divide zero by zero then
 
 
 
<math>0/0</math>
 
 
 
We know that the actual equation is <math>0^1/0^1 </math>
 
 
 
 
 
=<math>0^1/0^1 </math>
 
 
 
= 0^(1-1)                                                                              [Laws of Indices, <math>a^m/a^n = a^m-n </math>]
 
 
 
= <math>0^0 </math>
 
 
 
=<math>1 </math>                                                                                        [Already proven<ref>https://brilliant.org/wiki/what-is-00/</ref>]
 
 
 
 
 
So, the solution set(B) is a singleton set
 
 
 
 
 
set(B) =<math>\{1\} </math>
 
 
 
 
 
Now we can get a finite value to division of <math>0/0 </math> by taking intersection of both the solution sets.
 
 
 
Let the final solution set be <math>F </math>
 
 
 
 
 
<math>A\bigcap B </math> = <math>F </math>
 
 
 
<math>\{- \infty.....-3,-2,-1,0,1,2,3....\infty\}  </math> <math>\bigcap </math> <math>\{1\} </math>
 
 
 
<math>F </math> = <math>\{1\} </math>
 
 
 
 
 
Hence proving and deriving value of  <math>0/0 =1 </math>
 

Latest revision as of 17:03, 14 February 2025

Division of Zero by Zero, is a mathematical concept and is indeterminate.

Proof of Indeterminacy

We let $x=\frac{0}{0}$. Rearranging, we get $x\cdot0=0$ there are infinite solutions for this.


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