Open Real Interval/Examples/Example 1

Example of Open Real Interval

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

$I := \openint 1 2$

Then $3 \notin I$.


Proof

By definition of open real interval:

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

As $3 > 2$ it follows that $3 \notin I$.

$\blacksquare$


Sources

  • 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 2$: Continuum Property: Exercise: $\S 2.10 \ (1) \ \text{(i)}$
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.