Does infinite length strings lead to uncountable languages? This answer says:


  We can have uncountable languages only if we allow words of infinite length.


So does that means any (finite / infinite) language or any (finite / infinite) set of languages over any (finite / infinite) alphabet will be uncountable of words have infinite length?

Let me simplify this by asking specifically for the simplest language of infinite length string:


  Does the language of "finite" number of words, each of which can be of "infinite length" and are based on "finite" alphabet is uncountable?
A finite language is finite. Every finite set is countable, by definition.

A language of finite-length strings over a finite alphabet may be infinite but is always countable.

A language of infinite-length strings over a finite alphabet might be uncountable.