# What can I possibly be?

I'm open and not closed

or closed but not open.

If I'm not, though I can be,

open and closed

or neither closed nor open.

Hint: math

• I'm voting to close... or open... ARGH, I'M SO CONFUSED! ;-)
– Stiv
Nov 22, 2019 at 22:39
• Hopefully the answer is not related to body part of seniors..
– Alex
Nov 22, 2019 at 23:11
• @Alex rot13(vg vf abg) :) Nov 23, 2019 at 1:14

Sets? Because they can be open, closed, both or neither open or closed?

Are you a(n)

interval?

I'm open and not closed

If an interval does not contain its endpoints it is open.

or closed but not open.

A closed interval does contain its endpoints.

If I'm not, though I can be,

open and closed

A half-open interval contains only one of its endpoints.

or neither closed nor open.

A degenerate interval only consists of one real number.

Hint:

An interval in math is a set of (real) numbers lying between the extremities.

• hmm, this wasn't my original intention. The 'thing' could be both open and closed or neither closed nor open. I've edited the puzzle to reflect this clarification Nov 23, 2019 at 1:10
• @jazhang Next guess? Nov 23, 2019 at 1:22