Recent content by dark904

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...