Supremum and Infimum of a set - Find the Supremum (supS) and the infimum (infS) and indicate if supS is in the set S and if infS is in the set S:
S = {r in N: r^2 <= 15}
S = {r in Q: r^2 <= 15)}
S = {[(/1)^n][(n-1)/n]: n in N}
...
Real Analysis--Upper Semi-continuous Function - Show that if f is an upper semi-continuous function on a compact subset K of R^p with values in R, then f is bounded above and attains its supremum on K.
Edit:
R^p--Let p be a natural number an ...
Past analysis qualifying exam part 2 - I plan to take the analysis qualifying exam next time it is offered and I would like detailed solutions to a previous exam (some of the problems are fairly basic, but I would like to see solutions to ...
real analysis - assume that A And B are nonempty, bounded above and satisfy B subset or equal of A. Show that sup B<= sup A