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Division by $0$

What will be the answer if zero$(0)$ divided by zero$(0)$ Why It is un answerable?

$$\frac 00=\space ?$$ Thanks in Advance, Vicky


marked as duplicate by Douglas S. Stones, Pedro Tamaroff, Gerry Myerson, lhf, Asaf Karagila Nov 23 '12 at 12:10

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Because any number multiplied by $0$ gives $0$. So $a \times 0 = 0$ implies that $a = \frac{0}{0}$ for any a at all. So the answer is nonsense. So we simply say that $\frac 00$ is indeterminate form.

  • $\begingroup$ And indeed we say that the operation of dividing by 0 is prohibited in general. $\endgroup$ – Simon Hayward Nov 23 '12 at 11:11
  • $\begingroup$ thanks :) So we should not use division by zero at any instance $\endgroup$ – user1460692 Nov 23 '12 at 12:38
  • $\begingroup$ No, never. This was what caused so many problems when trying to put the calculus on to a rigorous footing. $\endgroup$ – Simon Hayward Nov 23 '12 at 12:40
  • $\begingroup$ Not "indeterminate form" but "undefined". The term "indeterminate form" is used in the context of evaluating limits, but the question is just about why the arithmetic operation of division is undefined with operands $0,0$. $\endgroup$ – Marc van Leeuwen Feb 13 '14 at 10:56

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