>minus times minus equals plus

>>9050609
>can't not equals can

>>9050609
1=1
1-1=0
-1(1+(-1))=0
-1*1+(-1)(-1)=0
-1+(-1)(-1)=0
(-1)(-1)=1

>>9050632
You're supposed to prove it for arbitrary x, not for 1

>>9050685
other person here, replace 1 with X and it'll still work

>>9050609
>0 divided by 0 is not 1

>>9050632
Mistakes.

>1=1
You arent allowed to make this expression; it is a tautology.

>1-1=0
Neither are you allowed to make this; it is definition of additive inverse -axiom.

>-1(1+(-1))=0
Incorrect. -X(X+(-X))=0 isn't always true.
E.g. x=-3, gives =18

>>9050685
Here's a generalized proof:
-x((-y)+y)=0
(-x)(-y)+(-x)(y)=0
(-x)(-y)-xy=0
(-x)(-y)=xy

>>9050840
>-X(X+(-X))=0 isn't always true.
>E.g. x=-3, gives =18
no it doesn't, idiot

-3(-3 + -(-3))
-3(0)
0

>>9050852
>Proof
>assumes definitions of multiplication, addition, and associativity of operations

>>9050840
>You arent allowed to make this expression; it is a tautology.

All equations are "tautologies" then, you dumb prick.

File: 446-pure-math-vs-applied-math.png (39KB, 473x226px) Image search: [Google]

39KB, 473x226px

>>9050609
-5 eggs = no eggs
-5 eggs + -5 eggs = still no eggs

If you don't have something, you can't have more of it if you don't have more of something. You have nothing.

>>9050840
>not allowed to state axioms in proof
do you understand what a proof is?

>>9050840
>Incorrect. -X(X+(-X))=0 isn't always true.
>E.g. x=-3, gives =18
Brainlet, it's 0

>>9050887
I was using the term colloquially.

>>9050840
I love cheap bait

>>9050961
Fair enough, "generalized proof" is so commonly used by uneducated twats.

>>9050887
Consider a ring R, with operations denoted by + and ·, the additive identity denoted by 0 and the additive inverse by -. We see that
[math]\forall x,\,y\in R\quad0=y+(-y)=(-x)\cdot(y+(-y))=(-x)\cdot y+(-x)\cdot(-y)=-(x\cdot y)+(-x)\cdot(-y)[/math]
Thus we see that -(x·y) and (-x)·(-y) are additive inverses, or, in other words, that
[math]\forall x,\,y\in R\quad x\cdot y=(-x)\cdot(-y)[/math]

But I still don't know if the ring has to be unital for this to hold.

>>9050906
No they're not. 1=1 is a tautology, while x=y is not because it depends on the values you enter.

>>9050615
Historically, double negatives in English were used for emphasis.

>>9050928
this is dumb and unrelated to the OP

>>9050609
yes
negative negates negative - what happens when negative is negated? It switches, it is positive. Thus:
>minus times minus equals plus