/sci/ - Science & Math

[Anonymous No.4993432]

Why do two negative numbers, when multiplied or divided by each other, become positive? Is there a proof for this concept?

[Anonymous No.4993450]

http://www.khanacademy.org/math/arithmetic/negative-numbers/v/why-a-negative-times-a-negative-is-a-p
ositive

[Anonymous No.4993451]

axiom 1:
1 + (-1) = 0

multiply with -1:

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

axiom 2:
1x = x

so

-1*1 = -1

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

thus from axiom 1:
(-1)*(-1) = 1

[Anonymous No.4993452]

Boils down to the elementary addition operation and the direction in which we do it on the numerical line.

[Anonymous No.4993458]

>>4993451
Multiplication used in proof of multiplication. Biting your own ass kind of logic right there.

[Anonymous No.4993460]

>>4993432
0*a=0
(1+(-1))a=0
a+(-1)a=0
(-1)a=-a

This can obviously be extended to all negative numbers by taking out -1 as a factor.

[Anonymous No.4993467]

Isn't anyone going to prove
-a*b = a*-b = -(a*b),
-a*-b = a*b,
for an arbitrary ring?

[Anonymous No.4993468]

>>4993458
where did i use any property other that 1x = 1, which is an axiom?

[Anonymous No.4993470]

>>4993460
what does this prove?

[OrganicEuphoria !C5Eg6mdVac No.4993473]

<div class="math">x=ab+(-a)(b)+(-a)(-b)</div>

Factoring out <span class="math">-a[/spoiler]

<div class="math">x=ab+(-a)[(b)+(-a)(-b)]</div>
<div class="math">=ab+(-a)(0)</div>
<div class="math">=ab+0</div>
<div class="math">=ab</div>

...and

Factoring out <span class="math">b[/spoiler]

<div class="math">x=[a+(-a)]b+(-a)(-b)</div>
<div class="math">=0\cdot b+(-a)(-b)</div>
<div class="math">=0+(-a)(-b)</div>
<div class="math">=(-a)(-b)</div>

<div class="math">x=ab</div>
<div class="math">x=(-a)(-b)</div>

Transitivity of equality,

<div class="math">ab=(-a)(-b)</div>

[Anonymous No.4993478]

>>4993473
again, multiplication used in proof of multiplication. Biting your own ass kind of logic right there.

[Anonymous No.4993477]

An axiom cannot be proven. It has to be believed.

[Anonymous No.4993495]

>>4993478
>>4993473

the proposition concerns the multiplication of two negative numbers

no statement in either post required axiomatically that (-x)*(-y) = xy

any mention of any multiplication ab where a or b > 0 is fine, as you're not proving multiplication, you're only proving that a negative times a negative is a positive

go be dumb somewhere else

[Anonymous No.4993497]

>>4993478
>>4993458

the proposition concerns the multiplication of two negative numbers

no statement in either post required axiomatically that (-x)*(-y) = xy

any mention of any multiplication ab where a or b > 0 is fine, as you're not proving multiplication, you're only proving that a negative times a negative is a positive

go be dumb somewhere else

[Anonymous No.4993502]

Soon the OP will ask why the square root of -1 is i and not -i.

The answer to both questions is: It is simply agreed upon. That's all there is to it. Our reasoning is shaped by the preponderance of our experiences. You really cannot "know" anything. Math is not "real", it is just something used to attempt to describe phenomena in the universe. Congratulations, OP, on realizing that logic is man-made and not from God. It dazed me for a while too.

All the numbers, symbols and shit you see here, are invented by hairy, stinking monkeys trying to figure out what sort of structure they live in. You, too, are a hairy, stinking monkey pondering about the meaning of existence, and so am I. However, the funny thing about philosophy is that it is a self-defeating concept; think what you would do if you DID figure out the meaning of life? It would mean there'd be nothing to ponder about, and you wouldn't be here pondering about it. Maybe that's why you are thinking of these things!

[OrganicEuphoria !C5Eg6mdVac No.4993504]

>>4993478
You don't know very much, do you?

[Anonymous No.4993514]

http://www.youtube.com/watch?v=rK4sXm_MPWo

http://www.youtube.com/watch?v=pzQY-9Nmtws

[Anonymous No.4993512]

>>4993497
>the proposition concerns the multiplication of two negative numbers
>multiplication
If the location of stupidity is somewhere else: why are you still here then?

[Anonymous No.4993526]

>>4993502
Sweet. Now I can use your post as a copypasta wallofbullshit against any valid question.

[Anonymous No.4993537]

>>4993478
Circular reasoning doesn't work like that. The assumptions he has made:

1 + (-1) = 0
f(x) = p(x) <=> c * f(x) = c * p(x)
Transitive property
x * 1 = x

That's it. Circular reasoning is when you use your desired result (or implications of desired result) as a premise. He didn't assume that (-1)(-1) = 1 in his process.

[Anonymous No.4993538]

>>4993502
Sorry, Mr. trytosoundsmart, the concept is not "simply agreed upon". The second post contains a link that explains the concept very clearly via the distributive property.

5(3 - 3) = 5(0) = 0

distribution
5(3) + 5(-3) = 15 + -15 = 0

[Anonymous No.4993544]

>>4993537

>multiply with -1:
>
>(-1)*(1) + (-1)*(-1) = 0

seems like using it

[Anonymous No.4993543]

Prove in an arbitrary ring that -a = -1*a for all a in the ring, where -1 is the additive inverse of the multiplicative identity.

[Anonymous No.4993552]

>>4993544
Are you trolling?
What he is trying to prove is that (-1)(-1) = 1, why the fuck would multiplying by -1 be disallowed? That's like trying to prove Pythagorean theorem without being able to use triangles or trigonometry.

Think before you respond.

[Anonymous No.4993559]

OP here. you have all been trolled harshly xD

[Anonymous No.4993560]

>>4993544
You're a fuckng retard and being obnoxious about it doesn't help.

[Anonymous No.4993561]

>>4993543
-a + a = 0.
-1*-a + -1*a = 0.
1*a + -1*a = 0.
a + -1*a = 0.
-1*a = -a.

[Anonymous No.4993571]

>>4993552
>What he is trying to prove is that (-1)(-1) = 1
(-1)(-1) is multiplying by -1 times two
>why the fuck would multiplying by -1 be disallowed
because you're using two negative numbers to show that two negative numbers multiplied result in positive

[Anonymous No.4993703]

>>4993571
That's true, but nowhere does he specify what this (-1)(-1) is equal to, it just sits there and ends up being equal to 1. If you still refuse to believe that proof, just give up and trust me, or everyone else on this board really.

[Anonymous No.4993886]

"negative numbers" are just symbols used to write formulas. The rules are selected for their simplicity, elegance and usefulness.

Rules for multiplying negative numbers follow from assumption that distributivity a*(b+c) = a*b+a*c holds.

[Anonymous No.4994083]

OP, just picture the whole thing as a rotation on the complex plane.

picture is addition, posting multiplication next.

[Anonymous No.4994098]

>>4994083

The notation Ae^(i*theta) is one of the three commonly used for complex numbers.

A = magnitude of vector in complex space
e = euler's constant
i = sqrt(-1)
theta = angle of vector in complex space

-1 is a complex number as well (-1 + 0i). So it also obeys these rules. Basically when you multiply -1 with -1 the product is a number that has been rotated 180 degrees (1). This applies to all negative numbers.

[Anonymous No.4994130]

[a+(-a)]=0
2[a+(-a)]=0
-2[a+(-a)]=0

[Anonymous No.4994215]

>>4993473

First line rewritten:

x = ab - ab + ab = ab

Second line rewritten:

x = ab - ab -a^2b = a^2b

In conclusion, one of us is retarded.

[Anonymous No.4994218]

>>4994215

First line rewritten:

x = ab - ab + ab = ab

Second line rewritten:

x = ab - ab -a^2b = -a^2b

In conclusion, one of us is retarded.

Fixed negative sign error.

[OrganicEuphoria !C5Eg6mdVac No.4994292]

I really don't know how to explain this anymore clearly than I have already done, through the above proof. However, because there's still seems to be some confusion, I'll try to clear things up.

<div class="math">-1\cdot -1=1</div>

Given, (please don't make me prove this...)

<div class="math">-1\cdot a=-a</div>

So,

<span class="math">0\cdot a=0[/spoiler]

Rewriting,

<div class="math">(1+-1)\cdot a=0</div>

Distributive property,

<div class="math">1\cdot a+-1\cdot a=0</div>

1 times any number is that number, right?

<div class="math">a+-1a=0</div>

As seen, the number that, when added to <span class="math">a[/spoiler] yields 0 is <span class="math">-a[/spoiler]

It follows that,

<div class="math">-1\cdot -1=-(-1)</div>
<div class="math">-1\cdot -1=1</div>

[Anonymous No.4994297]

>using math to prove math
This is why I dont respect math.

[OrganicEuphoria !C5Eg6mdVac No.4994306]

>>4994297

Solid, real solid reasoning right there.

[Anonymous No.4994311]

>>4994297
get out

[Anonymous No.4994318]

>>4993571
man you're dumb