Constructing a Sequence with Given Limit Points

th13teenj · Feb 19, 2011

Homework Statement

Let {y_j} be N given real numbers. Construct a sequence {a_n} so that {y_j} is the set of limit points of {a_n}, but a_n ≠ y_j for any n or j.

Bolzano-Weierstrass theorem

Have no idea how to go about it.

I'd really appreciate any help on this

lanedance · Feb 20, 2011

how about this, for the first n points, sequentially pick a point at a distance of from each of the yj,
for the next n, r/2 and so on.