# Is there a way to calculate the number of all the languages over an alphabet?

Let $$\Sigma = \{ a,b,c \}$$ be an alphabet.

How should I calculate the number of Languages over $$\Sigma$$?

• Note TeX "\sum" is used for sums (e.g., $\sum_{i=1}^n i$) whereas "\Sigma" should be used for a capital sigma. Also, the entirety of a TeX formula code should be between dollar tags; there's no need for a separate formula for every math symbol you write. See my edits. – dkaeae Apr 1 '19 at 9:40
• Hi, thanks for the edits. I will keep that in mind. – rsonx Apr 1 '19 at 15:42

There are the languages $$\{ a^0 \}$$, $$\{ a^1 \}$$, $$\{ a^2 \}$$, $$\{ a^3 \}$$ etc., which is already countable infinite.
But the powerset of the integers is uncountable infinite. So for every set S of integers, take the language $$\{ a^k: k \in S \}$$ and you have an uncountable infinite set.