# Stupid questions of basic analysis

• jessicaw
In summary, the argument is that if a sequence takes values in the real numbers and has a limit, the infimum is also the minimum and therefore greater than negative infinity. However, this is not always the case and the existence of a limit does not necessarily imply that the infimum is the minimum. It is a general fact that a sequence with a limit is bounded, and this can be proven by showing that only finitely many points can be a distance greater than 1 away from the limit.
jessicaw
Why $\lim t_n >-\infty\Rightarrow inf\{t_n:n\in\mathbb N\} >-\infty$?

I think the argument is, first of all, I assume $$\{t_{n}\}$$ take values in $$\mathbb{R}$$, then, due to the existence of limit, $$\inf$$ is indeed $$\min$$ and so it should be $$> - \infty$$. Somehow I think it is also an if-and-only-if statement.

Wayne

The existence of the limit does not imply infimum is minimum.

It's a general fact that if a sequence of points has a limit, the sequence is bounded. The proof can be sketched as follows: Only finitely many points can be a distance greater than 1 away from the limit (by the definition of a limit). So a lower bound of the set is either one of the values farther away than 1 from the limit, or one less than the limit is a lower bound

Argh, you are right.

I made a mistake in assuming that the bound can be attained within the finite set in the infimum but indeed it is not necessary true. Thanks.

Wayne

## 1. What is basic analysis?

Basic analysis is the process of examining and understanding the fundamental components of a system or problem. It involves breaking down complex concepts into simpler parts and analyzing them individually in order to gain a better understanding of the whole.

## 2. Why are some questions considered "stupid" in basic analysis?

Some questions may be considered "stupid" in basic analysis because they are too simple or obvious, or because they have already been answered or explained. These types of questions can be frustrating for experts who are well-versed in the subject matter.

## 3. How can asking "stupid" questions be beneficial in basic analysis?

Asking "stupid" questions can be beneficial in basic analysis because it can help to identify gaps in understanding, challenge assumptions, and spark new ideas. By asking questions that may seem obvious or simplistic, it can also help to clarify complex concepts for others.

## 4. What are some common mistakes people make in basic analysis?

Some common mistakes people make in basic analysis include assuming they already know the answer, not being open to new perspectives or ideas, and not thoroughly examining all components of a problem or system. It's important to approach basic analysis with an open mind and a willingness to learn.

## 5. How can one improve their basic analysis skills?

Improving basic analysis skills can be done through practice, asking thoughtful and insightful questions, actively listening to others, and being open to different perspectives and approaches. It can also be helpful to seek feedback from others and continuously learn about new methods and techniques for analysis.

Replies
1
Views
1K
Replies
2
Views
2K
Replies
3
Views
745
Replies
9
Views
2K
Replies
9
Views
2K
Replies
17
Views
3K
Replies
2
Views
652
Replies
2
Views
1K
Replies
2
Views
1K
Replies
4
Views
1K