Prove that a+a=a-(-a)

a+a = a-(-a)
subtract a-(-a) from both sides
a+a-a-(-a) = 0
the +a and the -a cancel out
a+0-(-a) = 0
now remove the 0 on both sides with division
(a+0-(-a))/0 = 0/0 =1
a/0+0/0-(-a)/0 = 1
0 + 1 -0 = 1
1 = 1

solved it

Prove negative numbers exist.

Oh that's right, you can't.

...

but you divided by zero

>doesn't know how to divide by zero

prove a+a=2a
a pile of things included with another pile of things is a pile of 2 things

a-a
remove a pile of things from a pile of things, no things.

a-(-a)
remove the removal of a pile of things from another pile of things results in a pile of 2 things

the opposite of exclusion is inclusion

>remove the removal of a pile of things from another pile of things results in a pile of 2 things

Removing the removal would leave you with just 1 pile of things. Not doing the action of removing the pile is not the same as adding another pile.

I'm sorry to tell you this, user, but you're retarded.

Imagine you're walking forward on a number line every time you add a number. When you hit a negative it's like turning around to walk the other way. Two negatives in a row makes you turn around twice and end up walking up the number line again.

He's not retarded. The "removal" metaphor was just bad.

i have a thing and get another thing = i have two thing

i have a thing and get rid of thing = i have no thing

i have a thing and not get rid of thing = i have a thing

This makes for me.

>binarity

makes sense*

a + a
= a + a + 0
= a + a + ((-a) - (-a))
= a + (a + (-a)) - (-a)
= a + 0 - (-a)
= a - (-a)

you're using the assumption that (-a) - (-a) = 0

you're begging the question

a+a=a+a
a+a-a=a
a+a=a-(-a)

Define n=-a
-a - (-a) = n - n = 0

>= a + (a + (-a)) - (-a)

What happened here?

This makes sense.

assumption? that's how subtraction is defined

>ē
nigger what

this question reduces to proving that (-1)*(-1) = 1

[math]
\begin{align*}
-1 * (-1 + 1) &= -1 * 0 \\
(-1)^2 + (-1) * 1 &= 0 \\
(-1)^2 &= 1
\end{align*}
[/math]

...

-(-a) -a = 0
adding a to both sides give you
-(-a) = a
So a -(-a) = a + a

The definition of a negative is that x - x = -x + x = 0

Substrate a from both sides
Multiply by -1 on both sides
Remove parentheses on right
Multiply by -1 again
a=a

Why is minus negative 1 the same as +1
yet ++1 does not equal negative one.

Negative numbers dont exist.

>forgot the QED brainlet

Negative numbers are a jewish construct to define debt. They didn't even exist as a concept until 200 years after jesus

add (-a) to both sides
a+a+(-a)=a-(-a)+(-a)
reduce inverses
a=a

prove runs in reverse

Yes, and why he shouldn't? it's reasonable to assume OP is working in some ring, where we know that for every x there is exactly one y (denoted by -x) st x+y=0

a + (-a) = 0
Therefore, a is the additive inverse of (-a)
hence: a = -(-a)
since a-(-a) is notation for a+(-(-a)) we have that
a-(-a) = a+(-(-a)) = a+a

a+ a = 2a
a-(a) = -2a
0 = 0
qaud demonstarum

yorue fucking retarded

>you're begging the question
you're right, here's the question. were you dropped on your head a lot?

a+a=a-(-a)
a+a=a+a
2a=2a

First of all,
>The reciprocal of -1 is -1 by definition so -1*-1 = 1.
>a=a*1 because 1 is the identity element for multiplication by definition
>a*(b*c) = (a*b)*c because multiplication is associative by definition
>(-1)*a = -a by the definition of additive inverse
>a + -a = a - a by the definition of subtraction

Now based on the above:
a + a = a + 1*a = a + (-1*-1)*a = a + (-1)*(-1*a) = a + -(-a) = a - (-a)

Let's start by assuming a and -(-a) are different values.
We know that for every element a in the real numbers there exists an element s.t. a-a=0 or for our purposes +(-a). Add that to both sides to yield: a+a+(-a) = a - (-a)+(-a). This gives a + (a+(-a))=a +0.
Means a+(-a)=0 or equivalently: a-a=a+(-a). Subtract -(-a) by the same logic of having an element to cancel the other you get a-a-(-a)=a+(-a)-(-a). Cancel the stuff on the left and right you end with -(-a)=a. Plug in and finish.

this thread is trash try harder
FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS FAGGOTS

brainlet spotted