Im having trouble solving these 2 questions:

1.

"Suppose (X,d) is a connected metric space, show that every continuous function f:X-->Z (set of integers with the standard metric) is constant"

and

2.

"Suppose (X,d) is a metric space and consider the two point metric space {0,1} with d_0(0,1)=1

Show the following are equivalent:

(a) (X,d) is disconnected

(b) There is a continous, non-constant function f:X--> {0,1} "