# Subsequential limit point

1. Aug 27, 2012

### CyberShot

1. The problem statement, all variables and given/known data

Determine all subsequential limit points of the sequence X_n = cos(n)

2. Relevant equations

Unsure of any.

3. The attempt at a solution

Tried determining subsequences of cos(n) but, having trouble finding any.

Can anyone tell me the definition and how to proceed?

Thanks!

2. Aug 27, 2012

### Staff: Mentor

The definition of what?

3. Aug 27, 2012

### CyberShot

The definition of subsequential limit point.

4. Aug 27, 2012

### Staff: Mentor

A limit point of a subsequence.

So that it doesn't appear that I'm being flip, here's an example to illuminate this concept. Consider an = cos(n * $\pi/2$), n ≥ 1.

The first few terms of the sequence: {0, -1, 0, 1, 0, -1, 0, 1, ...}

0 is a limit point of the subsequence {0, 0, 0, ... }.
Likewise, -1 and 1 are limit points of the subsequences {-1, -1, -1, ...} and {1, 1, 1, ...}, respectively.

5. Aug 28, 2012

### Bacle2

To give yet another perspective, consider your sequence as just a collection of

points. A collection of points may have more than one limit point ( or, of course,

no limit points or exactly one limit point). Informally, a subsequence is a subset of the

original sequence in which the order of the terms is preserved.