# Are all languages generate by Turing machines countable?

Are all languages generate by Turing machines countable? I know that the set of all TMs are countable, but what about the languages that they generate?

• What does it mean for a Turing machine to "generate" a language? Turing machines normally accept or decide languages. – David Richerby Dec 17 '14 at 8:29

Yes. All languages, not only those generated by Turing machines, are countable. This is because they are all subsets of $\Sigma^*$, and $\Sigma^*$ itself is countable. However, there are uncountably many languages.