Simple Apparent contradiction?

[Gamerex]

I came across this when doing another problem:

Suppose we have 2 numbers, (a+b) and (c+d), which both equal 0.

a+b=0
c+d=0

Then a+b=0=c+d,
Thus, a+b=c+d

However, a+b+c+d=0
Thus, a+b=-c-d

Therefore, a+b=c+d AND a+b=-(c+d)

How is this possible?

 

[chiro]

I came across this when doing another problem:

Suppose we have 2 numbers, (a+b) and (c+d), which both equal 0.

a+b=0
c+d=0

Then a+b=0=c+d,
Thus, a+b=c+d

However, a+b+c+d=0
Thus, a+b=-c-d

Therefore, a+b=c+d AND a+b=-(c+d)

How is this possible?

Hey Gamerex and welcome to the forums.

The simple answer is that -0 = +0 = 0. That's the basic argument for a problem like this.

 

[Curious3141]

I came across this when doing another problem:

Suppose we have 2 numbers, (a+b) and (c+d), which both equal 0.

a+b=0
c+d=0

Then a+b=0=c+d,
Thus, a+b=c+d

However, a+b+c+d=0
Thus, a+b=-c-d

Therefore, a+b=c+d AND a+b=-(c+d)

How is this possible?

No contradiction. The only solution to the equation x = -x is x = 0, which you can verify.

 

[Mentallic]

Therefore, a+b=c+d AND a+b=-(c+d)

How is this possible?

Therefore,

c+d=-(c+d)
2(c+d)=0
c+d=0

No problem there.