/sci/ - Science & Math

[Anonymous No.2743798]

Why does a negative multiplied by a negative equal a positive? inb4 "cuz its rule lol noob". I want the mathematical proof.

Pic semi-related: animated Pythagorean theorem proof

[Lord Fap !h3WDZNERS6 No.2743808]

I do not answer no stupid questions.

[Anonymous No.2743819]

>>2743808
My professor told me that there were no stupid questions.

[Anonymous No.2743824]

This is not a proof.

y=x is the same as y=-x*(-1)

y=-x*(-1)
y/(-1)=-x
-y=-x
y=x

[Anonymous No.2743830]

The reason is because changing one of the signs in a multiplication is supposed to give you the additive inverse of that multiplication. Therefore, if you change them both, you end up with the additive inverse of the additive inverse.

[Anonymous No.2743834]

>>2743819

there are and that's something that people tell stupid people.

[Anonymous No.2743842]

Symmetry.

Its an axiom, which means saying "its just a rule noob" is perfectly valid.

[Anonymous No.2743843]

I'm afraid I have a slightly boring answer OP: because that is what we choose it to be.

The real question here is what is -1 times -1 (because any negative number -a=(a)*(-1))

If we chose any other number for -1*-1 we would "break" mathematics. For example, if we said that (-1)*(-1)=-1, then -1*(-a)=-a which implies 1=-1 which is an absurdity (1 is the identity for multiplication, and there can only be one identity)

[Anonymous No.2743848]

>>2743798
copypasta from three days ago.

anyway, here:
http://en.wikipedia.org/wiki/Field_mathematics
for the reals (and or complex numbers) it can easy be shown by using the Associativity axiom and some left and right multiplication algebra.

/thread

[Anonymous No.2743849]

The last part can also be proven by the nw tau identity :DDDDDDDDDDDD

[Anonymous No.2743853]

(1) Zero times anything equals zero.

(2) Every number has exactly one additive inverse. This means if N
is a positive number, then -N is its additive inverse, so that
N + (-N) = 0. Likewise, the additive inverse of -N is N.

(3) We want negative numbers to obey the distributive law. This
says that

a*(b+c) = a*b + a*c.

(4) Now, we are forced to accept a new law, that negative times
positive equals negative. This is because we can use the
distributive law on an expression like

2*(3 + (-3)).

This equals 2*(0), which is zero. But by the distributive law,
it also equals

2*3 + 2*(-3).

So 2*(-3) does the job of the additive inverse of 2*3, and
therefore 2*(-3) is the additive inverse of 2*3. But the
additive inverse of 6 is just -6. So 2 times -3 equals -6.

(5) Next, we are forced to accept another new law, that negative
times negative equals positive. It's a lot like the example
in (4). We use the distributive law on, say,

-3*(5 + (-5)).

This is again equal to zero. But by the distributive law, it
also equals

-3*5 + (-3)*(-5).

We know the first thing, (-3*5) equals -15 because of the law
in (4). So (-3)*(-5) is doing the job of the additive inverse
of -15. We know -15 has exactly one additive inverse, namely 15.
Therefore,

(-3)*(-5) = 15.

[Anonymous No.2743854]

there are no stupid questions, only stupid niggers who ask them.

if x is a natural number, -x is defined to be the additive inverse of x. that is, x + -x = 0.

multiplication is distributive and all that, so if you multiply that equation by -y, where y is a natural number,

-y(x + -x) = -y * 0,

(-y * x) + (-y * -x) = 0.

(-y *x) is -yx. if you want a proof of that, i hate you.

so adding yx to both sides gives:
yx + -yx + (-y * -x) = yx + 0,

therefore
(-y * -x) = 0.

deal with it.

[Anonymous No.2743866]

negative 12 sets of negative 4

lack of a lack is a positive

[Anonymous No.2743883]

i made this thread as a troll three days ago

[Anonymous No.2743893]

i lose $10 dollars a day

how much more did i have three days back in time

(-3)*(-10)

[Anonymous No.2743911]

>>2743798
Here is a simple proof by contradiction:

If we adopted the convention that
(-1)(-1) = -1, the distributive property of multiplication wouldn't work for negative numbers:

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

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

0 = -2

Unless you know more advanced mathematics, these are the only kinda proofs you might be able to understand.

\thread

[Anonymous No.2743923]

>>2743798
Let n,m be positive. Then
0 = n * 0
0 = n * (-m + m)
0 = n*(-m) + n*m
-[n*m] + n*m = n*(-m) + n*m
-[n*m] = n*(-m)
This shows that n*(-m) = -(n*m) is negative.

Now the last statement.
0 = 0 * 0
0 = (-n + n) * (-m + m)
0 = (-n)*(-m + m) + n*(-m + m)
0 = (-n)*(-m) + (-n)*m + n*(-m) + n*m

Use the previous conclusion, cancel last two terms
0 = (-n)*(-m) + -(n*m) + -(n*m) + n*m
0 = (-n)*(-m) + -(n*m)
n*m + -(n*m) = (-n)*(-m) + -(n*m)
n*m = (-n)*(-m)
This shows that (-n)*(-m) = n*m is positive.

[Anonymous No.2743927]

>>2743883
How is this a troll?
You suck at trollin bro.

[Anonymous No.2743930]

idk why you are still arguing, the proof by complex polar form is enough.

[Anonymous No.2743950]

imo logically this doesnt stand, cause -2 * -2= -4
why?
because its like saying i owe 2$ 2 times, i owe totally 4 = -4

[Anonymous No.2743963]

Same troll back from a couple days ago.

inb4 /sci/ is the most easily trolled board, yet again

[Anonymous No.2743957]

>>2743930
It's pedagogically unsound to approach it that way. The above proofs for rings and fields holds in the general case. Your's assumes the complex definition of the exponential function, which is significantly more than you really need to prove it.

[Anonymous No.2744021]

I think it is easier if you think about it in terms of division. If you have -8/-2, there is 4 lots of -2 in the -8, so the answer is 4, and not -4.

[Anonymous No.2744038]

>>2743930
>>2743957
It's not just unsound, it's circular logic. In order to demonstrate the properties of the complex exponential function you would most likely use thousands of times the basic properties like (-x)*(-y) = x*y (even though you don't necessarily realize it since it's so natural).

[Anonymous No.2744056]

>>2744021
but m8, instead a pizza with 8 pieces you have a pizza that misses 8 pieces, if you divide the -8 with -2 you get -4 pieces of pizza.
I know mathematicaly -x *-x =x but intuitively doesnt work like that.

[Anonymous No.2744075]

>>2744056
>>2744056
>if you divide the -8 with -2 you get -4 pieces of pizza

WTF AM I READING!

[Anonymous No.2744079]

>>2743927
the thread made over a hundred posts of retarded argument. it was a great troll. especially as i'm a maths graduate

this thread however may be sincere, i neither know nor care

[Anonymous No.2744082]

>>2744056
>trollorstupid.jpg

[Anonymous No.2744090]

>>2744056
>-x*-x=x
No, -x*-x=x^2

[Anonymous No.2744096]

>>2744082
Ok sry, now that i thought it carefully it makes sense.
-8 / 2= 4
-8 / -2 = -4
because you do a divide, but negatively.
And no am not a troll, just trying to grasp maths, i was never good at it.

[Anonymous No.2744114]

>>2744096
So you're saying 4 x 2 = -8?

[Anonymous No.2744120]

>>2744114
No, i dont say or imply it in any way.

[Anonymous No.2744128]

oh sry, a typo.
Just reverse the -4 with 4.
I didn't saw it but it was in my mind that way.

[Anonymous No.2744138]

>>2744120
You say -8/2=4.
So obviously, using your logic, 4x2=-8.

[Anonymous No.2744143]

>>2744138
see
>>2744128
Ok lets end this thread.

[Anonymous No.2744148]

0/10
stop feeding the trol

[Anonymous No.2744200]

Using the axiomatic operations, consider <span class="math">ab+(-a)b+(-a)(-b)[/spoiler]. On the one hand

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

and on the other hand

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

Thus, we see

<span class="math">ab = ab+(-a)b+(-a)(-b) = (-a)(-b)[/spoiler]

and conclude

<span class="math">ab = (-a)(-b)[/spoiler]

QED