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Why can't it no be $\pm$ Infinity?

If $x/1$ is $x$ then $x/0$ should be $\pm$ Infinity.

user41758
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  • Down vote cause you dont know? – user41758 May 13 '14 at 11:03
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    You cannot divide by zero. Zero does not have a multiplicative inverse in the field of rational numbers (or real numbers, or complex numbers, or any field), because the existence of such an inverse would be inconsistent with the field axioms. – Paulistic May 13 '14 at 11:06
  • Did you check http://math.stackexchange.com/questions/556957/why-not-define-0-0-to-be-0 ? –  May 13 '14 at 11:07
  • @Paulistic ..Kind of like infinity? – user41758 May 13 '14 at 11:13
  • Other question does not answer why you cant use +- Infinity instead of undefined – user41758 May 13 '14 at 11:18
  • the expression $\frac{a}{b}$ is only shorthand for the formal expression $ab^{−1}$, where $b^{−1}$ is the multiplicative inverse of $b$. Since the field axioms only guarantee the existence of such inverses for nonzero elements, this expression has no meaning when $b$ is zero. As @jonnytan999 stated in his answer, $\frac{0}{0}$ could be anything..... But Just not with the axioms for maths we have today. – Paulistic May 13 '14 at 11:18

1 Answers1

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If x/y=z, z*y=x.
Agree?
For 0/0, we have z*0=0. z can be any number, thus 0/0 can be anything.