What is the flaw with this proof?

  • Thread starter soandos
  • Start date
  • Tags
    Proof
In summary, the conversation discusses the relationship between two equations, x == Sqrt[x] and 1 == Sqrt[0 + Sqrt[0 + Sqrt[x + Sqrt[0 + ...]]]], and how they are not equivalent. While the first equation implies the second, the reverse is not necessarily true. The conversation also uses an analogy to explain why this is the case.
  • #1
soandos
166
0
x==Sqrt[0+Sqrt[0+Sqrt[x+Sqrt[0+...]]]]
x==Sqrt[x]
x==1 and zero
1==Sqrt[0+Sqrt[0+Sqrt[x+Sqrt[0+...]]]]==0
1==0
 
Physics news on Phys.org
  • #2
soandos said:
x==Sqrt[0+Sqrt[0+Sqrt[x+Sqrt[0+...]]]]
x==Sqrt[x]
x==1 and zero
1==Sqrt[0+Sqrt[0+Sqrt[x+Sqrt[0+...]]]]==0
1==0

Your third line incorrectly assumes that any solution to the second line is a solution to the first line. This is not the case.

Consider
x = 7
x * 0 = 7 * 0
0 = 0, which holds for all x (including 2)
2 = 7
 
  • #3
I am not multiplying by zero in any step though, i am just saying that Sqrt[0+Sqrt[0+Sqrt[x+Sqrt[0+...]]]]==x
means that Sqrt[0+x]==x
 
  • #4
soandos said:
I am not multiplying by zero in any step though, i am just saying that Sqrt[0+Sqrt[0+Sqrt[x+Sqrt[0+...]]]]==x
means that Sqrt[0+x]==x

You are not multiplying by zero, correct. You are saying that line 1 implies line 2, which is a correct statement. You further claim (implicitly) that an x-value solving line 2 solves line 1, which is incorrect.
 
  • #5
why does it not follow?
 
  • #6
Why would it?

If someone is 52, then they're in their 50s. If someone is in their 50s, they might be 58. If someone is 58, they are eligible to join the 55+ club. But it doesn't follow that someone who is 52 might be able to join the 55+ club.

If x = -3 then x^2 = 9. If x^2 = 9 it follows that x is 3 or -3. But it does not follow that both 3 = -3 and -3 = -3.
 
  • #7
Just because the zeros of a function equal zero when put through the function, doesn't mean that the zeros equal each other.

(x+1)(x-1)=0
x=1;x=-1
1≠-1
 
  • #8
thanks.
btw epkid08, that is not what i was saying. i was saying that value of the function was x, not the zeros of f(x)
 
  • #9
soandos said:
thanks.
btw epkid08, that is not what i was saying. i was saying that value of the function was x, not the zeros of f(x)

It was an analogy. The message was that if x = {a,b}, a≠b.

x=√(x)
x={0,1}
0≠1
 
  • #10
epkid08 said:
It was an analogy. The message was that if x = {a,b}, a≠b.

x=√(x)
x={0,1}
0≠1

My message was that if F(x) --> G(x), and G(x) holds precisely for x in X, F(x) need not hold for all x in X.
 

1. What is the purpose of identifying flaws in a proof?

Identifying flaws in a proof is important because it helps ensure the accuracy and validity of the argument being presented. This is especially crucial in the field of science where incorrect conclusions can have serious consequences.

2. How do scientists typically go about finding flaws in a proof?

Scientists will carefully examine the assumptions, logic, and evidence presented in a proof to determine if there are any errors or inconsistencies. They may also conduct experiments or gather additional data to test the validity of the proof.

3. What are some common types of flaws that can be found in a proof?

Some common types of flaws in proofs include incorrect assumptions, faulty reasoning, insufficient or biased evidence, and mathematical errors. These flaws can lead to incorrect conclusions or unsupported claims.

4. Can a proof ever be considered completely flawless?

In science, it is generally accepted that no proof can be considered completely flawless. This is because new evidence or discoveries can always potentially challenge or improve upon existing theories and conclusions. However, a well-supported and thoroughly tested proof can be considered a strong and reliable explanation.

5. How can identifying flaws in a proof contribute to the advancement of science?

Identifying flaws in a proof can lead to a better understanding of a particular phenomenon or concept, and can also inspire further research and experimentation. It can also help prevent the spread of misinformation and promote the development of more accurate and reliable theories and explanations.

Similar threads

  • Linear and Abstract Algebra
Replies
4
Views
1K
  • Linear and Abstract Algebra
Replies
7
Views
915
  • Linear and Abstract Algebra
Replies
1
Views
698
  • Linear and Abstract Algebra
Replies
25
Views
1K
  • Linear and Abstract Algebra
Replies
3
Views
982
  • Linear and Abstract Algebra
Replies
4
Views
1K
  • Linear and Abstract Algebra
Replies
11
Views
1K
  • Linear and Abstract Algebra
Replies
5
Views
1K
  • Linear and Abstract Algebra
2
Replies
41
Views
3K
  • Calculus and Beyond Homework Help
Replies
14
Views
247
Back
Top