are these sets countable

• Sep 30th 2008, 01:33 AM
szpengchao
are these sets countable
[0,1]

{0,1,2,...,9}^N

N is the set of natural number
• Oct 1st 2008, 06:50 PM
ThePerfectHacker
Quote:

Originally Posted by szpengchao
[0,1]

Not this is $2^{\aleph_0}$.

Quote:

{0,1,2,...,9}^N
$10 = {0,1,...,9}$ and $2\leq 10$ thus $|2^{\mathbb{N}} | \leq |10^{\mathbb{N}}|$.
Thus, it cannot be countable.