Why is my proof wrong? (analysis)

In summary, the conversation discusses the values of sine function and upper and lower darboux sums. The speaker is trying to prove something but encountered an error and is looking for assistance. They mention the values of 1 and -1 for the sine function, and then discuss the formulas for the upper and lower darboux sums. However, there seems to be some confusion around the summations and the value of -12. The speaker also mentions an epsilon value but it is unclear what it represents. They are seeking clarification on their mistake.
  • #1
Artusartos
247
0
I was trying to prove this, but something went wrong and I'm not sure what...

We know that the greatest value of sin(1/x) can be 1 and the lowest value can be -1...

We know that the upper darboux sum is...

[tex]U(f,P) = sup(f[t_{k-1} , t_t]) (t_k - t_{k-1}) = (1) (1-(-1)) = 2[/tex]


We also know that the lower darboux sum is...

[tex]L(f,P) = inf(f[t_{k-1} , t_t]) (t_k - t_{k-1}) = (-1) (1-(-1)) = -12[/tex]

So we know that...

[tex]U(f,P) - L(f,P) = 2 - (-2) = 4 > \epsilon[/tex]

Can anybody tell me where I went wrong?

Thanks in advance
 
Physics news on Phys.org
  • #2
What are you trying to prove in the first place??

And don't there need to be summations in the [itex]U(f,P)[/itex] and [itex]L(f,P)[/itex]?? How did you choose P anyway?

I also don't see where -12 comes from. Did you mean -2?

What is [itex]\epsilon[/itex] supposed to be?
 

FAQ: Why is my proof wrong? (analysis)

Why am I getting a different result from my expected outcome?

This could be due to a mistake in your calculations or an error in your assumptions. Double check your work and make sure all of your assumptions are accurate.

How do I know if my proof is valid?

A valid proof should follow the rules of logic and be supported by evidence and mathematical principles. You can also ask for feedback from other scientists or experts in the field.

What should I do if I can't find a mistake in my proof?

If you have carefully checked your work and still can't find a mistake, you can try approaching the problem from a different angle or seeking help from others. It's also possible that your proof is correct and you just need to provide more evidence to support your argument.

How can I improve my proof writing skills?

Practice and feedback are key to improving your proof writing skills. It's also helpful to study and learn from well-written proofs and to seek guidance from experienced scientists.

Can I still publish my findings if my proof is wrong?

It's important to be honest about the validity of your proof. If it is incorrect, it's best to revise and improve it before publishing. However, if you have already published your findings, you can publish a correction or retraction to ensure the accuracy of the scientific record.

Similar threads

Show |x^2 sin^8(e^x)| <= (16 pi^3)/3
Replies
7
Views
3K
Proving piecewise function is k-differentiable
Replies
5
Views
962
Fundamental Theorem of Calculus
Replies
1
Views
1K
Prove ##|\{ q\in\mathbb{Q}: q>0 \} |=|\mathbb{N}|##.
Replies
3
Views
1K
How to prove that ##M_i =x_i## in this upper Darboux sum problem?
Replies
10
Views
1K
I Original definition of Riemann Integral and Darboux Sums
Replies
14
Views
3K
Prove every subset of countable set is either finite or else countable
Replies
1
Views
1K
Do these two statements imply an underlying induction proof?
Replies
7
Views
864
Can the Sequence of Upper Darboux Sums Converge to the Upper Darboux Integral?
Replies
1
Views
1K
Can anybody explain this to me? (Analysis)
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top