[thaumasiotes]

> You’re asserting that negative one times X is itself negative which is in fact what the article is attempting to prove in the first place

Absolutely not. The article explicitly postulates this:

> We also take for granted the fact that the product of a positive real number and a negative real number is a negative real number

You're right that that's the interesting part of the question, but as far as the article is concerned, it's just an uninteresting assumption.