Simple Apparent contradiction?

  • Context: High School 
  • Thread starter Thread starter Gamerex
  • Start date Start date
  • Tags Tags
    Contradiction
Click For Summary

Discussion Overview

The discussion revolves around a mathematical scenario involving two equations, (a+b) and (c+d), both equating to zero. Participants explore the implications of these equations and the apparent contradiction that arises when considering both the equality and the negation of the sums.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the equations a+b=0 and c+d=0, concluding that a+b=c+d and a+b=-c-d, questioning how this is possible.
  • Another participant suggests that the resolution lies in the fact that -0 = +0 = 0, indicating that there is no contradiction.
  • A different participant asserts that the only solution to the equation x = -x is x = 0, implying that this resolves the apparent contradiction.
  • Another response reiterates the conclusion that c+d=-(c+d) leads to 2(c+d)=0, reinforcing that c+d must equal 0 without identifying any contradiction.

Areas of Agreement / Disagreement

Participants generally agree that there is no contradiction in the mathematical reasoning presented, but they express this agreement through different explanations and approaches. The discussion remains somewhat unresolved as participants offer varying perspectives on the implications of the equations.

Contextual Notes

The discussion does not delve into potential limitations or assumptions regarding the definitions of the variables or the context of the equations.

Gamerex
Messages
25
Reaction score
0
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?
 
Mathematics news on Phys.org
Gamerex said:
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.
 
Gamerex said:
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.
 
Gamerex said:
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.
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
3K
Replies
7
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 19 ·
Replies
19
Views
4K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 13 ·
Replies
13
Views
3K