Function

Question

Determine whether f is a function from the set of all bit strings to the set of integers if f(S) is the smallest integer i such that the ith bit of S is 1 and f(S)=0 when S is the empty string ,the string with no bits.

Answer 1

The necessary criteria which must be satisfied by every function is that it must be defined for every element in the domain and it must map one element from domain to only one element in range (A unique mapping).

In this case the domain is the set of all bit strings and range is the set of Nonnegative Integers.

The said function is not defined for every bit string which contains only 0's.

So we conclude it is not a function.