Show that the set of all bit string (string of 0’s and 1’s) is countable.

To show that the set of all bit strings (strings of 0's and 1's ) is countable.

Given information:

N={1,2,3...}S={the set of all bit string}

Concept used:

One to one: Every element in domain must be mapped with element in codomain.

Calculation:

Let the set of all bit strings be S then show that there exists a bijective function from N to S to show that the S is countable.

N={1,2,3,.....}S={the set of all bit strings}

Define a map f from N to S and show that ¡t is both one-one and onto to show that the set S is countable.

f(n)=Binary representation of n, where n∈N.

Now show that the function f defined above is a bijective function.

Firstly, show that the function f is one-one