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Is it zero, undefined, infinity, or ERR09 :)

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Is it zero, undefined, infinity, or ERR09 :)

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symbolipoint

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matt grime

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HallsofIvy

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What in the world is "ERR09"? A calculator notation?Is it zero, undefined, infinity, or ERR09 :)

If you are talking about dividing 1 (or any other non-zero number) in the Complex number system or any of its subfields, then "1/ 0" is just an error- you don't do it. It is true that the

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matt grime

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First, a priori, the axioms of a field (at least those normally given) do not state that 0 does not have a multiplicative inverse. It is, however, easy to deduce from the axioms that one must define 0*x=0 for all x, and one cannot cancel zeroes.

But there are more things than just fields. In the extended complex plane the symbols x/0 are defined for all non-zero x (and are equal to the symbol [itex]\infty[/itex]. Division by zero is still not the inverse of multiplication, though.