Mistake in my analysis book ? Or am I missing something ?

In summary, the conversation discusses a theorem and its implications on a bounded set. The theorem states that a continuous function on a closed interval is uniformly continuous there. The conversation also mentions that the bounded subset may not necessarily be a closed interval, and provides an example of a bounded set composed of rational numbers.
  • #1
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Homework Statement



Please review the attachment.

Why can L be OUTSIDE of D ?

[tex] x_n \in D[/tex] and D is bounded. So doesn't that mean that any subsequential limit of [tex]x_n[/tex] has to be in D ? Btw, Theorem 3.10 is Bolzano Weierstrass.
Theorem 4.4 Says that A continuous function on a closed interval is uniformly continuous there.
 

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  • #2
I think I understand now.

They said that D is bounded by not closed. i.e suppose D = (a,b)

[tex] x_{n_k} \to a[/tex] could happen and a in not in D.

Is this correct ? Anyone ?
 
  • #3
What you said is right. Also, the bounded subset need not be an interval of reals; for example, the subset could be all the rational numbers from 0 to 2. Then there are an uncountable number of points not in the set that are the limit of Cauchy sequences inside the set.
 
  • #4
Perfect. Thanks.
 

Related to Mistake in my analysis book ? Or am I missing something ?

1. What should I do if I find a mistake in my analysis book?

If you find a mistake in your analysis book, it is important to first identify the type of mistake and its impact on your overall analysis. If it is a minor error, you can simply correct it and make a note of the correction. However, if the mistake significantly affects your results, it is important to discuss it with your colleagues or supervisor for further investigation and potential revision of your analysis.

2. How can I prevent making mistakes in my analysis book?

To prevent making mistakes in your analysis book, it is important to double check your work and have someone else review it as well. Additionally, following a standardized and organized method for recording and analyzing data can also help reduce the chances of making mistakes. Keeping detailed notes and documenting any changes or corrections can also be helpful in preventing errors.

3. What should I do if I am unsure if there is a mistake or I am missing something in my analysis book?

If you are unsure about a potential mistake or if you are missing something in your analysis book, it is best to consult with your colleagues or supervisor. They may offer fresh insights or be able to identify any potential issues that you may have overlooked. Additionally, you can also review your methods and data to ensure that you have not missed any important steps or information.

4. Is it normal to have mistakes in my analysis book?

Yes, it is normal to have mistakes in your analysis book. As with any scientific work, there is always room for error. However, it is important to identify and correct any mistakes to ensure the accuracy and validity of your analysis. Collaboration and open communication with your colleagues can also help catch and prevent mistakes.

5. What are the consequences of having a mistake in my analysis book?

The consequences of having a mistake in your analysis book can vary depending on the severity of the error and its impact on your results. In some cases, it may require a revision of your analysis and potentially delay the publication of your work. It is important to address and correct any mistakes to maintain the integrity of your research and ensure accurate conclusions.

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