Half-Open Real Interval/Examples/Example 1

Example of Half-Open Real Interval

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

$I := \hointr 1 2$

Then $1 \in I$.

Proof

By definition of open real interval:

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

As $1 \le 1$ it follows that $1 \in I$.

$\blacksquare$

Sources

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