Hi Dick, thanks for the speedy response.
For part b, I understand that there are subsets of R that aren't intervals, however by the problem's definition of "roominess," the only subsets of R which are roomy are open intervals, as it is impossible for a y > 0 such that (x -y , x + y) \subseteq...
Homework Statement
This problem starts with a definition,
A set S \subseteq R is said to be roomy if for every x \in S, there is a positive distance y > 0 such that the open interval (x - y, x + y) is also contained in S.
Problems based on this definition:
a) Let a < b. Prove that the...