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

Re:Why don't we define “imaginary” numbers for every “imposs... by afiori on Monday April 10, 2023 @08:33AM (#35511525)

let ϴ = 0/0 then 1ϴ = ϴ = 0/0 = (00)/0 = 0(0/0) = 0ϴ it follows 1 = 0

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Re:Why don't we define “imaginary” numbers for every “imposs... by xigoi on Monday April 10, 2023 @09:34AM (#35512077)

This is assuming that Θ interacts with arithmetic operations the usual way (that is, ℝ ∪ {Θ} is a field), which the person you're replying to did not say.

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Re:Why don't we define “imaginary” numbers for every “imposs... by afiori on Monday April 10, 2023 @10:22AM (#35512671)

True, but the point of giving a "value" to 0/0 is to use it somehow.

For example in the context of limits you define a whole lot of number like values like 0+ or 0- that are useful wrt operations on limits.

I was trying to give an example of how ℝ ∪ {Θ} has almost no advantages compared to just ℝ

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Re:Why don't we define “imaginary” numbers for every “imposs... by tshaddox on Monday April 10, 2023 @05:31PM (#35517644)

Sure, but the whole "problem" we were trying to solve was that zero doesn't interact with arithmetic operations the usual way.

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