Proving A_n Converges to 0: Real Analysis

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Homework Help Overview

The discussion revolves around proving the convergence of a sequence \( A_n = (a, a, a, a, \ldots) \) to a limit, specifically in the context of real analysis. The sequence involves vectors in \( \mathbb{R}^p \) and the original poster expresses confusion regarding the nature of convergence in this setting.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of convergence in relation to sequences of vectors, questioning whether the sequence converges to zero or to the vector \( a \). There is a discussion about the nature of points in \( \mathbb{R}^p \) and the implications of treating \( a \) as a vector rather than a point.

Discussion Status

The discussion is ongoing, with participants clarifying misunderstandings about the problem statement and the nature of the sequence. Some guidance has been offered regarding the use of the distance function to analyze convergence, but no consensus has been reached on the correct interpretation of the problem.

Contextual Notes

There is a note that the original poster may have misstated the problem, indicating a potential misunderstanding of the convergence concept in the context of sequences of vectors. The discussion is framed within the constraints of a homework help environment.

junior33
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prove [tex]\ A_n = ( a, a,a,a,a,...)[/tex] converges to zero. [tex]a \in \ R^p[/tex]

Been reading this real analysis book before i take it next semester and been a lil stuck on this question. I am probably making it seem more difficult than it is. Most of the questions had examples in the chapter but this one didnt. can some one help me out?
 
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If A_n = (1_1,1_2,...1_p) then A_n is constantly point with coordinates 1. This An will NOT converge to 1, it will converge to the constant itself.

i think you are confusing a point in R^p with the sequence itself a point in R^p is a set of p real numbers where the order in which each of these numbers follow each other matters.
a itself is NOT a point in R^p.
 
it says that the a's are vectors in [tex]a \in \ R^p[/tex]

would it be that same
 
sorry, that's correct. the a's ARE vectors. sorry i thought you thought they were coordinates of the vectors in the sequence.

well use the distance function u have and choose N=1 for any epsilon. see what happens.
 
First, as the sticky at the top of this section says, this is NOT the place for homework. I am moving it to the homework section.

Second, you misstated the problem in the body of your post. You do NOT want to prove "that (a, a, a, a, ...) converges to 0" because, in general, it doesn't. You want to prove that it converges to a. Okay what is |a- a|?
 
^^^ yes that's what i meant
 

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