Why don't we define “imaginary” numbers for every “impossibility”? (2012)

Re:Why don't we define “imaginary” numbers for every “imposs... by ndsipa_pomu on Monday April 10, 2023 @10:28AM (#35512758)

The most common definition of division being the inverse of multiplication.

if b ≠ 0 then the equation a/b = c is equivalent to a = b × c. Assuming that a/0 is a number c, then it must be that a = 0 × c = 0. However, the single number c would then have to be determined by the equation 0 = 0 × c, but every number satisfies this equation, so we cannot assign a numerical value to 0/0

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Re:Why don't we define “imaginary” numbers for every “imposs... by amitport on Monday April 10, 2023 @10:57AM (#35513110)

Thanks, this definition does seem problematic. In any case, it is not the only possible way and in a/0=c, c does not have to be defined as a real number. We can defined it as similarly to complex number with new rules that do not collide with existing reals.

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Re:Why don't we define “imaginary” numbers for every “imposs... by ndsipa_pomu on Monday April 10, 2023 @11:33AM (#35513554)

There's a couple of mentions in other comments about the Riemann Sphere (https://en.wikipedia.org/wiki/Riemann_sphere) which does define division by zero, but sacrifices the numbers forming a field under addition and multiplication.

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