Answer to Question #213093 in Real Analysis for Nikhil

Question #213093

-2 is the limit point of the interval ]-3,2[.

True or false with full explanation


1
Expert's answer
2021-07-06T15:55:19-0400

A limit point is a point for which every neighbourhood contains at least one point belonging to a given set.


Given the closed interval [-3,2], the point -2 is a limit point for the interval, since we can find a neighbourhood of -2 which completely lies in the interval.


Considering the above given closed interval, A neighbourhood of -2 is the open interval (-2.5,1). We can find a "\\epsilon>0" (a small number) such that


"-2 \\in (-2.5, 1) \\subset (-2.5- \\epsilon, 1+ \\epsilon) \\subset [-3,2]"

Hence,

-2 is the limit point of the interval [-3,2].


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