1. ## Notation question

Hey,

I would like to prove that $\displaystyle \left\{0,1\right\}^{\mathbb{N}}$ is uncountable. My first question is what the notation $\displaystyle \left\{0,1\right\}^{\mathbb{N}}$ means precisely (I am not familiar with the notation).
I am only asking someone to clarify the notation and NOT to help with the proof (I would like to have a crack at it myself and then return if I get stuck).

Thanks.

2. ## Re: Notation question

Originally Posted by detalosi
Hey,

I would like to prove that $\displaystyle \left\{0,1\right\}^{\mathbb{N}}$ is uncountable. My first question is what the notation $\displaystyle \left\{0,1\right\}^{\mathbb{N}}$ means precisely (I am not familiar with the notation).
I am only asking someone to clarify the notation and NOT to help with the proof (I would like to have a crack at it myself and then return if I get stuck).
If each of $A~\&~B$ is a set then $B^A$ stands for the set of all functions from $A$ to $B$.

In this case $\displaystyle \left\{0,1\right\}^{\mathbb{N}}$ is the set of all bit-strings. That is the set of all sequences with only 0's & 1's as entries.