Diagonalization method in theory of computation

 

Diagonalization Method

To prove set is uncountable.

∑={a,b}

∑* is countable

2^∑* is uncountable.

∑*={દ,a,b,aa,ab,bb,ba,aaa,aab----------------------------------}

Prove  2^∑* is uncountable  prove by contradiction.

Let  2^∑*   is countable.

  and let languages is 

L1={ɛ,a}

L2={a,b}

L3={ɛ,a,aa}

L4={ab,b,ba}

L5={aa,ba,bb}

L6={ɛ,aaa}

L={110000}

L'={001111}

language 001111 is not belong to   2^{∑* .}

languag so prove by contradiction    2^∑*   is uncountable.