Simple Apparent contradiction?

In summary, the conversation discusses the possibility of two numbers, (a+b) and (c+d), both being equal to 0. It is shown that this is possible through the equations a+b=0 and c+d=0, and that there is no contradiction in the solution of a+b=c+d AND a+b=-(c+d). The solution to this problem is that -0 = +0 = 0.
  • #1
Gamerex
25
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?
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5


This is a great question and it highlights the importance of understanding the context and assumptions in mathematical equations. In this case, the apparent contradiction arises because we are assuming that both (a+b) and (c+d) equal 0, but we are using different operations to arrive at that result.

In the first equation, we are simply stating that (a+b) and (c+d) both equal 0. However, in the second equation, we are adding (a+b) and (c+d) together to get 0. This means that we are assuming that (a+b) and (c+d) have opposite signs, which is why we end up with the equation a+b=-c-d.

So, while it may seem contradictory at first, it is important to remember that the second equation is built on different assumptions than the first. This highlights the importance of clearly defining our variables and assumptions in mathematical equations to avoid confusion and contradictions.
 

Related to Simple Apparent contradiction?

1. What is a simple apparent contradiction?

A simple apparent contradiction is a statement or situation that initially appears to be contradictory or impossible, but upon further examination, can be explained or resolved.

2. How do you distinguish between a simple apparent contradiction and a real contradiction?

In a simple apparent contradiction, there may be a misunderstanding or missing information that can be resolved. In a real contradiction, there is a fundamental inconsistency or conflict that cannot be reconciled.

3. Can a simple apparent contradiction be proven or disproven?

No, a simple apparent contradiction is not a statement or hypothesis that can be proven or disproven. It is a perception or interpretation that can be examined and potentially resolved.

4. Is it common for scientific research to encounter simple apparent contradictions?

Yes, simple apparent contradictions can arise in many areas of scientific research, especially when dealing with complex systems or phenomena. They can often lead to new insights and discoveries.

5. How do scientists approach resolving a simple apparent contradiction?

Scientists use critical thinking, logical reasoning, and evidence-based methods to carefully examine the perceived contradiction and find a resolution. This may involve conducting further experiments, gathering more data, or revisiting and refining existing theories.

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