How Does Every Convergent Subsequence Prove the Limit of a Sequence?

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In summary, the phrase "should be easy but I'm confused" is used to express frustration or difficulty in understanding or completing a task that is expected to be simple. This can be overcome by breaking the task into smaller parts and seeking assistance from others. Feeling confused about something that "should be easy" is normal and can be avoided by approaching tasks with an open mind and recognizing individual differences in learning.
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davitykale
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Homework Statement



Prove that lim a_n = L given that (a_n) is a sequence defined such that every subsequence has a convergent that converges to L\in R

Homework Equations



Bolzano-weierstrass and the works

The Attempt at a Solution



A subsequence of a subsequence is just a subsequence of the original sequence, so if I can show that (a_n) is bounded. Can I do something with maybe 2L as a bound?
 
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I'd really appreciate any help I could get :)
 
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Related to How Does Every Convergent Subsequence Prove the Limit of a Sequence?

1. What does "should be easy but I'm confused" mean?

The phrase "should be easy but I'm confused" is a common expression used to convey a feeling of frustration or difficulty in understanding a concept or completing a task that is expected to be simple or straightforward.

2. Why do people say "should be easy but I'm confused"?

People may say "should be easy but I'm confused" because they are struggling to comprehend or complete something that they believe should be simple or easy based on their previous knowledge or experience.

3. How can I overcome confusion when something "should be easy"?

To overcome confusion when something "should be easy," it can be helpful to break the task or concept down into smaller, more manageable parts. Additionally, seeking clarification or assistance from others can also aid in understanding and reducing confusion.

4. Is feeling confused about something that "should be easy" normal?

Yes, feeling confused about something that "should be easy" is completely normal. It is common for people to encounter unexpected challenges or complexities when trying to understand or complete tasks that they believe should be simple.

5. How can I avoid feeling confused about things that "should be easy"?

To avoid feeling confused about things that "should be easy," it can be helpful to approach tasks or concepts with an open mind and a willingness to learn. It is also important to recognize that everyone learns and understands things differently, and what may be easy for one person may not be for another.

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