no, just at least one..

Let us consider the set

. Since it is bounded, there is an

such that

.

Bisect

into

and

.

At least one of these has the properties:

1. intersection with

is not empty; and (WHY?)

2. Infinite (WHY?)

Name that set

. Again, bisect

into

and

. again, at least one of these has the properties:

1. intersection with

is not empty; and (WHY?)

2. Infinite (WHY?)

Name that set

..

Do this continuously and form the sequence of nested intervals

.

Use the Property of Nested interval,

such that

for all

.

... now, can you do the rest? you only need to show that every neighborhood of

contains infinitely many points from

and hence from

. (maybe, two steps or three more.. Ü)