Question

non zero real numbers is not a interval in line. why?

Answer 1

Say again?

Answer 2

why non-zero real numbers is not a interval?

Answer 3

the set of all non zero real numbers is not an interval why?

Answer 4

Well an interval implies continuity but if you exclude zero then you break that continuity so you have: \[\mathbb{R}^+ = \mathbb{R} / \left\{ 0\right\} = (-\infty,0) \cup (0, \infty)\] But zero is EXCLUDED.

Answer 5

so natural numbers is not an interval?

Answer 6

Nope. They are a set because they are composed of discrete components:
\[\mathbb{N} = \left\{1,2,3,4,...\right\}\]

Answer 7

Well, the answer to your question is yes. But they are NOT an interval.

Answer 8

superb thanks mr.malevolence19