Cardinality of \mathbb{R}^{\mathbb{N}} - Is it \mathbb{R} or \{0,1\}?

[jostpuur]

What's the cardinality of $$\mathbb{R}^{\mathbb{N}}$$?

It must be $$\mathbb{R}$$ or $$\{0,1\}^{\mathbb{R}}$$, but I'm not sure which.

 

[Hurkyl]

Arithmetic to the rescue!

R^N = (2^N)^N = ...