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The proof constructs a monotone bounded sequence. It thus converges. Dividing into three intervals is to rule out the case where both (closed) intervals contai
by backlava 13y ago
The proof constructs a monotone bounded sequence. It thus converges. Dividing into three intervals is to rule out the case where both (closed) intervals contain the point.
- Tloewald 13y agoRight. There's no reason for the intervals to be closed that I can see.
- ColinWright 13y agoYou're right, there isn't, but when you use open intervals you'd be surprised how many people get worked up over the fact that some of the points have been omitted. It's easier to avoid the question entirely. It tends only to be people who already know a lot about this that come up with the objections or comments you're making, and usually they realise that actually, yes, it all works.