The set B is given by
B = { n/n+1 | n = a natural number } as a subset of the Real numbers. Is this set
i) Open
ii) Closed
Provide justification.
The set is not open. Note, but if we choose small enough then does not lie in , take for example .
The set is not closed. We need to show that its complement is not open. Let be its complement. Since it means but not interval lies completely outside because converges to .