Question

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

True or false with full explanation

Answer 1

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 $\epsilon >0$ such that:

$$-2 \in (-2.5,1) \sub (-2.5-\epsilon,1+\epsilon) \sub [-3,2]$$

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