Question

Let S be the set of all string of 0' s and 1' s,and define
D:S→Z as follows:For all s∈S,

D(x)=the number of 1' s in s minus the number of 0' s ins.

a.Is D one-to-one?Prove or give a counterexample.

Answer 1

S must be the set of finite strings of 0's, 1's

Answer 2

for all s->S. is it??

Answer 3

D(x) would not be defined if you had an infinite string of 0's and 1's

Answer 4

@perl is there any reason ???

Answer 5

D is not 1-1