- #1

kindlychung

- 12

- 0

## Homework Statement

Is it possible to construct a sequence like this? If yes, please construct one, if not, give a proof. See the attached pic for requirements for the sequence to be constructed.

## Homework Equations

NO

## The Attempt at a Solution

I know how to construct a sequence that has subsequences that converge to a finite number of limits, such as:

1, -1, 1, -1, ...

1, 2, 3, 1, 2, 3, ...

This problem brings the sine function to my mind, but since R is uncountable, it's not possible to build a sequence that contains terms that has a 1-1 correspondence with sin(x).

I might as well ask: what is the cardinality of [tex]N \times N [/tex]?

[tex] card N \times N = card N ? [/tex]

In that case I could just repeat the sequence {1, 1/2, 1/3, ...} over and over again.