Closed Real Interval/Examples/Example 1
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Examples of Closed Real Intervals
Let $I$ be the closed real interval defined as:
- $I := \closedint 1 3$
Then $3 \in I$.
Proof
By definition of open real interval:
- $I = \set {x \in \R: 1 \le x \le 3}$
As $3 \le 3$ it follows that $3 \in I$.
$\blacksquare$
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 2$: Continuum Property: Exercise: $\S 2.10 \ (1) \ \text{(v)}$