>>9527513>Suppose P, derive absurdity, therefore not P.Are you saying this is the proof by contradiction? I would agree.
This is how most reductio ad absurdums are used by mathematicians.
Let me try to rephrase this. A reductio absurdum used by a mathematician is typically
True proof:
Suppose P, therefore C, prove this exists
Reductio ad absurdum:
Suppose X, therefore C, prove this exists, is absurd.
The way I've worded it is important, because in order to prove something is absurd, you must assume everything you've assumed in the first case. In your example, the first think you asserted is only part of how a reductio ad absurdum is utilized by mathematicians. There are other ways, as I've stated. Typically the true construction proofs are not reductios at all as you've pointed out, but once we breach the territory of having to explain that the situation where NO hyperbolas could be constructed is possible it's not as simple as just assuming P, then deriving the absurdity.
But the funny thing about this is that even if it were, your overall point is incorrect. In this case either they use my example of a reductio ad absurdum or they use yours. Either way you slice it it's NOT a proof of negation.
