Interior, Closure, Boundary and Cluster Points of a Set

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Homework Help Overview

The discussion revolves around the concepts of closure, interior, boundary, and limit points of the set [0,1). Participants are exploring definitions and properties related to these concepts in the context of set theory and topology.

Discussion Character

  • Conceptual clarification, Assumption checking, Exploratory

Approaches and Questions Raised

  • The original poster attempts to identify the closure, interior, boundary, and limit points of the set, expressing uncertainty about the limit points. Some participants question the definitions and implications of limit points, while others explore the convergence of sequences within and outside the set.

Discussion Status

The discussion is active, with participants providing feedback on the original poster's attempts and raising further questions about the nature of limit points. There is an exploration of different interpretations regarding convergence and the potential for limit points outside the set.

Contextual Notes

Participants are considering the definitions of limit points and the implications of sequences converging to points within and outside the set [0,1). There is an acknowledgment of the need to clarify these definitions further.

LauraLovies
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Homework Statement


Find the closure, interior, boundary and limit points of the set [0,1)


Homework Equations





The Attempt at a Solution



I think that the closure is [0,1]. I believe the interior is (0,1) and the boundary are the points 0 and 1. I think the limit point may also be 0. I do not know, however, if I am on the right track.
 
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The first three are right. Better review your definition of a limit point, though.
 
any suggestions? a limit or cluster point is where a sequence converges...would it converge to 1 or the whole set?
 
To what possible points can a sequence in [0,1[ converge?
 
to any point within the set?
 
Yes, so any point of [0,1[ are limit points.
Are there other points to which a sequence may converge?
 
i am sure there are other points outside of the set which are limit points for sequences in the set
 
So, which points?
 
im not really sure...maybe the complement of the set?
 

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