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With your ordering, what is the least element of the open interval (0,1)?
by v64 9y ago
With your ordering, what is the least element of the open interval (0,1)?
- mrmyers 9y agoAh, right. Makes sense.
- nerdponx 9y agoWhat if you order the absolute values of the differences from the midpoint of the interval, where the midpoint is supremum - infimum if bounded, or zero if unbounded? Obviously this fails for closed/open sets like [a,infinity), but wouldn't it work for fully open sets?
- v64 9y agoUltimately, the point becomes moot because we focus too much on "normal" sets. Such a definition does nothing to help us answer questions like, what is the least element of the irrationals?