#Countable or Uncountable

Question

Prove that set of all the languages are uncountable?

Answer 1

i think question is incomplete bcoz

let $\sum$=$(a,b)^{*}$ and language be set all string such that|w|=2 so string will be=aa,ab,ba ,bb .it is countable so how can we say that all language is uncountable.

Answer 2

Let ∑={a,b} ====> ∑* = (a+b)*

Every language is a collection of strings

Therefore L ⊆ ∑*

Collections of all languages means every  subset of ∑*

Therefore powerset of  ∑* is the set of all languages.

We know that,  ∑* is countable set

There are One property of countable sets says that, power set of countable set is uncountable.

Comments

I am asking about the proof of that property....can u plz provide?

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I just remember that property... U can google it.. And the read the PDF.