Unbounded Closed Real Interval/Examples/Example 1

Example of Unbounded Closed Real Interval

Let $I$ be the unbounded closed real interval defined as:

$I := \hointl \gets 3$

Then $2 \in I$.

Proof

By definition of open real interval:

$I = \set {x \in \R: x \le 3}$

As $2 \le 3$ it follows that $2 \in I$.

$\blacksquare$

Sources

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