Applying the definition of uniformly continuous, for given we can find a such that if and then .
We can find such that if , then .
The question:
Suppose is uniformly continuous. Show that if { } is a Cauchy sequence in (a,b], then { } is always a Cauchy sequence.
So I need to show that . I have then written out the definition for g being uniformly continuous on (a,b] but I can't see where to go from this definition to show the Cauchy sequence. Help?