Is it possible to solve a fraction that has 0 at denominator?Can a 0 be defined or solved?

Question

Is it possible to solve a fraction that has 0 at denominator?Can       a    0   be defined or solved?

Izabella Fisher · Accepted Answer

Let one equation -      4    0    =  xThen   4  =  0  ×  xBut no value would work for x because 0 times any number is 0. So division by zero doesn&#039;t work.

Tarnayfu · Accepted Answer

Algebraically, the projective numbers are convenient, which adds a single point at   ∞ (in particular,   ∞  =  −  ∞ in this number system), and defines   a      /    0  =  ∞ whenever   a  ≠  0You have to keep in mind, however, that   0      /    0 is still undefined, and so are   ∞      /    ∞,   ∞  +  ∞, and   ∞  −  ∞Projective coordinates may be enlightening; let   (  a  :  b  ) (for real   a  ,  b) denote the projective number   a      /    b. Alternatively, we can define coordinates without reference to   ∞, by saying that   (  a  :  b  )  =  (  c  :  d  ) if and only if   a  d  =  b  c, and then define   ∞  =  (  1  :  0  )Then, the elementary arithmetic operations are  (  a  :  b  )  +  (  c  :  d  )  =  (  a  d  +  b  c  :  b  d  )  (  a  :  b  )  −  (  c  :  d  )  =  (  a  d  −  b  c  :  b  d  )  (  a  :  b  )  ⋅  (  c  :  d  )  =  (  a  c  :  b  d  )  (  a  :  b  )      /    (  c  :  d  )  =  (  a  d  :  b  c  )  (  a  :  b      )          −      1        =  (  b  :  a  )In projective coordinates,   (  0  :  0  ) is not allowed, so any arithmetic operation that would give that result is instead left undefined.There is an even more general theory called &quot;wheel theory&quot; that would let us further extend to allow   0      /    0 to be a number as well. They&#039;re kinda neat, but I am not aware of wheels being used beyond the work of their inventor.

Is it possible to solve a fraction that has 0 at denominator? Can a/0 be defined or solved?

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