Hi, I need help with the following proof question for my stats course. It states:

On the real line consider the collection of left-open/right-closed intervals:

a) Write each of (0,1) and {0} explicitly as monotone limits of elements, in .

b) For the 's chosen in a), determine the lower and upper sequences

and

c) In general if , n = 1,2,... is monotone prove that it does indeed converge and, explicitly, that

if and

if

d) Let so it is clear that

For provide both its upper and lower sequences as in b) and thus prove whether or not converges.

Thanks a lot. I'm trying really hard to wrap my head around this stuff. : )