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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 an

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 https://en.wikipedia.org/wiki/The_Crystal_Maze

creddit 7y ago
What does this analogy have to do with multiplication?
- soVeryTired 7y ago
  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.
  - creddit 7y ago
    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 7y ago
      > 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.

creddit 7y ago

What does this analogy have to do with multiplication?

soVeryTired 7y ago
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.
- creddit 7y ago
  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 7y ago
    > 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.