Proving the Validity of My Mathematical Proof

  • Thread starter Unassuming
  • Start date
  • Tags
    Proof Work
In summary, the conversation discusses whether a sequence that is not diverging is equivalent to converging. It is pointed out that this may not be the case as the sequence could be oscillating and only bounded. The proof presented by the original poster is questioned and it is suggested that N_2 may be redundant. It is also discussed that the contradiction in the proof may not be valid. Ultimately, it is concluded that a sequence that does not have the property of being arbitrarily small is divergent.
  • #1
Unassuming
167
0
Does my "proof" work?

n\in \mathbb{N}
\).
 
Last edited:
Physics news on Phys.org
  • #2


not diverging may not be equivalent to converging. it may be merely bounded but oscillating. so i would contradict boundedness rather convergence. maybe by showing that the difference between the nth and the n+k is larger than any bound.
 
  • #3


xaos said:
not diverging may not be equivalent to converging. it may be merely bounded but oscillating.
But such a sequence is certainly diverging / not converging.


About the proof presented in the OP: isn't your N_2 redundant? After all, n+1 > n >= N_1. Other than this minor quibble, your proof is fine.
 
  • #4


morphism said:
But such a sequence is certainly diverging / not converging.


About the proof presented in the OP: isn't your N_2 redundant? After all, n+1 > n >= N_1. Other than this minor quibble, your proof is fine.

I thought something was wrong with my proof. I was wondering whether N_2 was redundant. I can repeat the definition using N_1 again, or N.

I was wondering about the contradiction though. Does it really contradict? I proved the opposite based off the assumption, therefore I can assume the original is correct?
 
  • #5


You showed that for any convergent sequence (a_n), the quantity |a_{n+1} - a_n| can be made arbitrarily small (by choosing sufficiently large n). This means that a sequence for which this cannot happen is divergent.
 
  • #6


ahh, thank you
 
  • #7


yeah my first guess is usually wrong. you would think that divergence is always unbounded.
 

What is the process for proving the validity of a mathematical proof?

The process for proving the validity of a mathematical proof typically involves carefully examining each step of the proof and ensuring that it follows logical and mathematical principles. This may include checking for errors, verifying the accuracy of any assumptions, and providing clear and concise explanations for each step.

What are some common strategies for proving the validity of a mathematical proof?

Some common strategies for proving the validity of a mathematical proof include using mathematical induction, proof by contradiction, and direct proof. These methods involve using logical reasoning and mathematical principles to demonstrate the validity of the proof.

How can I ensure that my mathematical proof is correct?

To ensure that your mathematical proof is correct, it is important to carefully review each step and make sure that it follows logical and mathematical principles. It can also be helpful to seek feedback from peers or experts in the field to identify any potential errors or areas for improvement.

What should I do if I encounter a problem or error in my mathematical proof?

If you encounter a problem or error in your mathematical proof, it is important to carefully review each step and try to identify where the error may have occurred. If you are unable to find the error on your own, it may be helpful to seek feedback from peers or experts in the field.

What is the importance of proving the validity of a mathematical proof?

Proving the validity of a mathematical proof is crucial in ensuring that the results and conclusions drawn from it are accurate and reliable. It also helps to build a strong foundation for future mathematical research and advancements in the field.

Similar threads

  • Calculus and Beyond Homework Help
Replies
7
Views
302
  • Calculus and Beyond Homework Help
Replies
3
Views
624
  • Calculus and Beyond Homework Help
Replies
13
Views
627
  • Calculus and Beyond Homework Help
Replies
1
Views
434
  • Calculus and Beyond Homework Help
Replies
1
Views
522
  • Calculus and Beyond Homework Help
Replies
1
Views
399
  • Calculus and Beyond Homework Help
Replies
1
Views
439
  • Calculus and Beyond Homework Help
Replies
3
Views
451
  • Calculus and Beyond Homework Help
Replies
3
Views
743
  • Calculus and Beyond Homework Help
Replies
24
Views
617
Back
Top