# Subsequential limit point

## Homework Statement

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

Unsure of any.

## 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!

Mark44
Mentor

## Homework Statement

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

Unsure of any.

## 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!

The definition of what?

The definition of what?

The definition of subsequential limit point.

Mark44
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.

Bacle2