Question

Give an example of an open set which is not an interval

Answer 1

The real numbers except zero is one useful example, more generally the union of two disjoint open intervals is not an interval but is open.

Follow-up exercises:
why is the first one useful (where does it turn up)? Why is the second one open but not an interval?

Hope it helps...

Answer 2

The real numbers except zero(0) is one useful example.

Step-by-step explanation:

To give, an example of an open set which is not an interval =

The real numbers except zero(0) is one useful example.

The generally the union of two disjoint open intervals is not an interval but is an open.

Example: (0, 1) ∪ (2, 3)

Hence, the real numbers except zero(0) is one useful example.