why is the product of two negative quantities is a positive quantity?

[unbiased]

I have forgotten my maths. Can somebody help me in remembering the proof, as to how two negative quantities make a positive quantity as a result of their product?

 

[Bassyhead]

I don't think I've seen a formal proof for this, but consider:

4 * 3: Multiplication is just repeated adding. You cumulatively add 3 to itself 4 times (or vice versa) to yield 12.

-4 * -3: This time, you subtract -3 from itself 4 times. Because the '4' is negative, you subtract instead of adding. Subtracting a negative number is the same as adding, so that's why you get a postiive number.

 

[BrownTown]

interesting that "Highly Technical" apparently refers to stuff you learn in grade school

 

[sao123]

Proof 1

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)

Hence, by the transitivity of equality, we have

ab = (-a)(-b).



Proof 2
Assume -1 = (-1)(-1),
Using the distributive propery or multiplacation we write

(-1)(1 + -1) = (-1)(1) + (-1)(-1)

(-1)(0) = -1 + -1

0 = -2

 

[MrDudeMan]

Originally posted by: BrownTown
interesting that "Highly Technical" apparently refers to stuff you learn in grade school

good contribution :thumbsup:

Just FYI, all of that "simple math" you learn in grade school can have a complicated formal proof. Being a smartass for no reason earns you no respect in HT.

For example - The Fundamental Theorem of Algebra

Euler, Lagrange, and Laplace couldnt even solve it. They came up with some of the most brilliant math in history too. A lot of what you learned in grade school that is "too stupid" to be discussed in HT is derived from the FTOA.

 

[suszterpatt]

Originally posted by: BrownTown
interesting that "Highly Technical" apparently refers to stuff you learn in grade school

Math as a science is not what you learn in grade school. If I asked someone what natural numbers are, chances are he couldn't tell me a mathematically correct answer. Btw, can you?

 

[Bassyhead]

Originally posted by: BrownTown
interesting that "Highly Technical" apparently refers to stuff you learn in grade school

I guess you didn't learn politeness while you were in grade school.

 

[Navid]

Originally posted by: unbiased
I have forgotten my maths. Can somebody help me in remembering the proof, as to how two negative quantities make a positive quantity as a result of their product?

A: n= -m or -n = m

B: -1 X n = -n

C: Replace -n in B with its equivalent (m) from A ---> -1 X n = m

D: Replace n in C with its equivalent (-m) from A ---> -1 X -m = m

 

[unbiased]

Thanks a lot guys.