Minus times minus

[jack]

Can you remember when you first learnt/understood that a negative number times a negative number gave a positive number?

Did you think that makes sense? Did you think it should be negative, or were you just not sure?

I'm sure I'd learnt the rule before then, but I remember working out an explanation for why it makes sense (imagine you give out numbers of merits or demerits to people; taking back a number of demerits is the same as giving that number of merits). Before then, I didn't see why it should be positive, though I don't think I thought it should be be negative, I just didn't understand why.

Conversely, some people think the other way round. Negative Math: How Mathematical Rules Can Be Positively Bent. I haven't read all of his book, so I don't know if it's a good explanation of why and how mathematical rules are chosen, or if he's smoking bad weed. It could be either.

I do know it made me queasy. He seems to think minus times minus giving minus is more obvious, and perhaps should be standard, and that mathematics is a conspiracy against this.

Comments

[cornute.livejournal.com]

My teacher explained it this way.

You're a photographer and a friend of yours asks your help on some photos. She's losing [[3 pounds a week]] and wants a pictorial record, one picture a week.

After a few weeks, she gets discouraged, and says "I don't feel like anything has changed!"

"Look!" you say, "Here are the last [[5 weeks]]' pictures. If we go through them backwards, week to week, we can see you gain 15 pounds!*"

This is perfectly intuitive in a story, and it's then that the teacher explained that it demonstrates "negative 3 times negative 5 equals positive 15."

*this line is given for the purposes of mathematics only. Do not actually use this line on any friends who are attempting to lose weight.

given for the purposes of mathematics only. Do not use on any friends who are trying to lose weigh

[cartesiandaemon.livejournal.com]

ROFL.