In particular, it is incorrect to say that a ÷ 0 is infinity. The argument that any number a, divided by a very small one, becomes extremely large is unconvincing: a negative number a divided by a small positive number does not become large, and neither does a positive number a divided by a small negative number.
Another way to see why division by zero does not work is to work backwards from multiplication, remembering that anything multiplied by zero is zero. So
It is possible to disguise a division by zero in a long algebraic argument, leading to such things as a spurious proof that 2 equals 1.
It is both possible and meaningful to find the limit as x approaches 0 of some divisions by x; see l'Hopital's rule for some examples.
For the complex plane, see also Pole (complex analysis).
Many computer architectures produce a runtime exception[?] when an attempt is made to divide by zero.
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