## Metric spaces f:X --> Z

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} "