(October 13, 2013 at 10:27 am)Aractus Wrote: There is no real-world example for negative numbers, debt or otherwise. Debts are bank bonds/contracts, they're not negative money, money is not negative bank bonds/contracts. Currency and Bonds don't even behave the same way! You can't go into a store, buy your groceries, and in leiu of payment be given a bond.

Sure you can. It's called a gift certificate. And if you don't think a debt is negative money, look at your bankbook. See all those little (-) signs? That's money that you used to have, but no longer have. They are losses to your buying power.

Or does "real world" only mean things you can poke with a stick? If so, math itself doesn't exist. You're not saying that, are you?

boolean logic

The easier "proof" of 4 * -5 = -20 is:

4 * -5 = -5 + -5 + -5 + -5 = -20 (it follows from the axiom a + -a = 0)

From that, you can prove that -5 * -4 = -20 by using the following (stolen) proof:

Let a and b be any two real numbers. Consider the number x defined by

x = ab + (-a)(b) + (-a)(-b).


We can write

x = ab + (-a)[ (b) + (-b) ] (factor out -a)
= ab + (-a)(0)
= ab + 0
= ab.

Also,

x = [ a + (-a) ]b + (-a)(-b) (factor out b)
= 0 * b + (-a)(-b)
= 0 + (-a)(-b)
= (-a)(-b).

So we have

x = ab
and
x = (-a)(-b)

Therefore

ab = (-a)(-b).

There is a real and simple answer to this. Go back to first grade. Remember the number line?

5 means five units to the right - right is the default.

5*4 means you go five units to the right four times, and end up at 20.

-5 means five units to the left. The negative sign reverses direction.

(-5)*4 means you go 5 units to the left four times, and end up at -20.

With (-5)*(-4), the first minus reverses direction from the default right and has you going left. The second minus reverses direction again, and has you going right.

(October 13, 2013 at 3:31 pm)bennyboy Wrote: Or does "real world" only mean things you can poke with a stick? If so, math itself doesn't exist. You're not saying that, are you?

Um, yes, that's exactly what I've already said. Numbers are not real quantifiable things, and although we can draw comparison between positive numbers in real life, we cannot do that with negative quantities.

Quote:That's money that you used to have, but no longer have.

I'm not arguing that you can't negative from your quantity of real money, I'm stating a simple fact: you cannot hold a negative quantity of anything physically in your hand. A bond isn't money and it isn't negative money, and money isn't a bond or a negative bond, you're just deciding to use them as opposites for your example.

Let me ask you this, when you are in debt who has the bond - you or the bank? Can you withdraw the bond from an ATM and have money go IN to your account by doing so?

Money is real, debt isn't. If you think that debt is as real as money then explain to me how the GFC happened...

(October 16, 2013 at 7:37 am)Aractus Wrote: I'm stating a simple fact: you cannot hold a negative quantity of anything physically in your hand.

True dat! If you try to hold a piece of -109 degree F dry ice in your hand it will burn the crap out of you, and if you try to hold a negative weight helium balloon it'll float away!

Wow! All this convoluted mathsy stuff.

It's really simple.

Two wrongs make a right.

Right?

(October 16, 2013 at 12:44 pm)DLJ Wrote: Wow! All this convoluted mathsy stuff.

It's really simple.

Two wrongs make a right.

Right?

Wrong!
Wrong!

(October 16, 2013 at 1:13 pm)pocaracas Wrote:

(October 16, 2013 at 12:44 pm)DLJ Wrote: Wow! All this convoluted mathsy stuff.

It's really simple.

Two wrongs make a right.

Right?

Wrong!
Wrong!

Don't be so negative.

(October 16, 2013 at 1:15 pm)DLJ Wrote:

(October 16, 2013 at 1:13 pm)pocaracas Wrote: Wrong!
Wrong!

Don't be so negative.

Oh... wasn't that a positive?