4 ms·

uh, (-1) * (-1) = 1 holds in any ring. If you have multiplication distributing over addition, then the product of (-1) and (-1) is 1 . It isn't an arbitrary c

by drdeca 5y ago

uh, (-1) * (-1) = 1 holds in any ring. If you have multiplication distributing over addition, then the product of (-1) and (-1) is 1 . It isn't an arbitrary choice.

not2b 5y ago
Here's a physical example for those who have trouble intuitively grasping why the product of two negative numbers is positive. Let's say we have a water tank. We can fill it by opening a faucet on the top, or drain it by unplugging the bottom. For simplicity let's say that if we fill it we add 1 liter per minute, and if we drain it we lose 1 liter per minute (or equivalently, add -1 liter per minute). Q1: if we open the top faucet for 2 minutes, how much water do we add? 1 liter/min times 2 minutes: 2 liters. Q2: if we open the bottom faucet for 2 minutes, how much water do we add? -1 liter/minute times 2 minutes, -2 liters. What about the volume two minutes ago? That would be -2 minutes, right? So suppose the drain was open, how much more water did we have -2 minutes from now, or 2 minutes ago? -2 times -1: 2 liters more.
Qem 5y ago
It's arbitrary. It causes our math to be asymmetrical, dominated by negative numbers. It could be the reverse, positive-dominated, and there's even proposals to make it symmetric. See https://www.scirp.org/journal/paperinformation.aspx?paperid=111530 https://www.scirp.org/journal/paperinformation.aspx?paperid=...
- drdeca 5y ago
  In what sense is it "dominated by negative numbers"? Half of the combinations of multiplying gives something positive and half gives something negative. That's balanced. If someone fails to count (+,-) and (-,+) separately, they're just counting wrong. Complaining that this is asymmetric is like complaining that even/odd is asymmetric, on the basis that "even plus even is even, and odd plus odd is even, but only if one is even and the other is odd, is the result odd. This is unbalanced in favor of producing even numbers".
nh23423fefe 5y ago
-1 * -1 = 1 -1 * x = -1 * x + 0 = -1 * x + -x + 1*x = (-1 + 1)*x + -x = -x

by drdeca 5y ago

uh, (-1) * (-1) = 1 holds in any ring. If you have multiplication distributing over addition, then the product of (-1) and (-1) is 1 . It isn't an arbitrary choice.

not2b 5y ago

Here's a physical example for those who have trouble intuitively grasping why the product of two negative numbers is positive. Let's say we have a water tank. We can fill it by opening a faucet on the top, or drain it by unplugging the bottom. For simplicity let's say that if we fill it we add 1 liter per minute, and if we drain it we lose 1 liter per minute (or equivalently, add -1 liter per minute). Q1: if we open the top faucet for 2 minutes, how much water do we add? 1 liter/min times 2 minutes: 2 liters. Q2: if we open the bottom faucet for 2 minutes, how much water do we add? -1 liter/minute times 2 minutes, -2 liters. What about the volume two minutes ago? That would be -2 minutes, right? So suppose the drain was open, how much more water did we have -2 minutes from now, or 2 minutes ago? -2 times -1: 2 liters more.

Qem 5y ago

It's arbitrary. It causes our math to be asymmetrical, dominated by negative numbers. It could be the reverse, positive-dominated, and there's even proposals to make it symmetric. See https://www.scirp.org/journal/paperinformation.aspx?paperid=111530 https://www.scirp.org/journal/paperinformation.aspx?paperid=...

drdeca 5y ago
In what sense is it "dominated by negative numbers"? Half of the combinations of multiplying gives something positive and half gives something negative. That's balanced. If someone fails to count (+,-) and (-,+) separately, they're just counting wrong. Complaining that this is asymmetric is like complaining that even/odd is asymmetric, on the basis that "even plus even is even, and odd plus odd is even, but only if one is even and the other is odd, is the result odd. This is unbalanced in favor of producing even numbers".

nh23423fefe 5y ago

-1 * -1 = 1 -1 * x = -1 * x + 0 = -1 * x + -x + 1*x = (-1 + 1)*x + -x = -x