[soVeryTired]

I've always thought the best way to explain this was by analogy with the '90s TV show "The Crystal Maze" [0].

Contestents are put in a dome filled with gold and silver tickets being blown around by fans. For every gold ticket they collect, they get a point. For every silver ticket, they lose a point. If they collect enough points, they win a prize.

Sorting through the team's collection of tickets and throwing away a silver ticket (minus a -1) is just as good as adding another gold ticket (+1).

Not sure the kids these days are down with the crystal maze though. More loss to them - Richard O'Brien was a national treasure.

[0] https://en.wikipedia.org/wiki/The_Crystal_Maze

[_2d30]

What does this analogy have to do with multiplication?

[soVeryTired]

It shows that subtracting a minus one is equivalent to adding a plus one. The one logical leap that isn't explicitly spelled out is that subtracting X is the same as adding (-1)X. But I'm pretty sure that's the definition of integer multiplication.

[_2d30]

I see how it’s intuition for addition/subtraction but that doesn’t tell us much about multiplication. 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 so by explicitly supposing that, your analogy isn’t useful.

[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.