Closed Real Interval/Examples/Example 1

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: $\S 2.10 \ (1) \ \text{(v)}$
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