On: A proof of proof by infinite descent

[gerdesj]

Taking the square root of -1 is not only an irrational thing to do but bloody daft. QED 8)

i tends to pop out as a construction so I suspect you can probably prove it is both rational and irrational or neither, depending on the fine print.

Here's a discussion: https://math.stackexchange.com/questions/823970/is-i-irratio...

[BalinKing → gerdesj]

I doubt you'd be able to prove that it's rational, regardless of how it's constructed, since wouldn't that imply that it's also (for example) a real number?

[lupire → BalinKing]

That's the point. When you use ambiguous definitions, you get stuck in a morass.

[BalinKing → lupire]

Still, I don't see how any such definition could even be called a "definition of √-1" in the first place, since the resulting object wouldn't actually have the properties of √-1.