# How many decision problems do exist?

Are there countable infinte decision problems or uncountable infinite?

Thank you

• A decision problem on a alphabet (i.e. non-empty finite set) $\Sigma$ is some subset $P\subseteq \Sigma^*$ (i.e. $P\in\mathcal P(\Sigma^*)$). So it's uncountable (because $\mathcal P(\Sigma^*)$ is). – xavierm02 Jan 20 '17 at 14:23