38 // Heron Suit

that this is a reasonable thing to aim for, if only for mathematical elegance. If we require the usual laws to be valid, then

ðþ2Þ6ðÀ3Þ þ ðÀ2Þ6ðÀ3Þ ¼ ð2 À 2Þ6ðÀ3Þ ¼ 06ðÀ3Þ ¼ 0

so

À6 þ ðÀ2Þ6ðÀ3Þ ¼ 0

Adding 6 to both sides, we find that

ðÀ2Þ6ðÀ3Þ ¼ þ6

In fact a similar argument justifies taking ðþ2Þ6ðÀ3Þ ¼ À6, as well.

Putting all this together: mathematical elegance leads us to define minus times minus to be plus. In applications such as finance, this choice turns out to match reality in a straightfor- ward manner. So as well as keeping arithmetic simple, we end up with a good model for important aspects of the real world.

We could do it differently. But we'd end up by complicating arithmetic, and reducing its applicability. Basically, there's no contest. Even so, `minus times minus makes plus' is a conscious

........................................... human convention, not an inescapable fact of nature.

Heron Suit

No cat that wears a heron suit is unsociable.

No cat without a tail will play with a gorilla.

Cats with whiskers always wear heron suits.

No sociable cat has blunt claws.

No cats have tails unless they have whiskers.

Therefore:

No cat with blunt claws will play with a gorilla.

Is the deduction logically correct?

...........................................

Answer on page 262

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