Open Real Interval/Examples/Example 2

Example of Open Real Interval

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

$I := \openint 0 2$

Then $2 \notin I$.

Proof

By definition of open real interval:

$I = \set {x \in \R: 0 < x < 2}$

As it is not the case that $2 < 2$ it follows that $2 \notin I$.

$\blacksquare$

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 2$: Continuum Property: Exercise: $\S 2.10 \ (1) \ \text{(iv)}$