Open Real Interval/Examples/Example 1

Example of Open Real Interval

Let $I$ be the open real interval defined as:

$I := \openint 1 2$

Then $3 \notin I$.

Proof

By definition of open real interval:

$I = \set {x \in \R: 1 < x < 2}$

As $3 > 2$ it follows that $3 \notin I$.

$\blacksquare$