3 ms·
Depending on the context unbounded and infinite may mean very different things, for example the surface of a sphere being unbounded but finite.
by danbruc 13y ago
Depending on the context unbounded and infinite may mean very different things, for example the surface of a sphere being unbounded but finite.
- gohrt 13y agoA sphere is bounded but infinite* http://en.wikipedia.org/wiki/Compact_space http://en.wikipedia.org/wiki/Compact_space *Infnite cardinality of points, not infinite in measure.
- jerf 13y agoThat's why I didn't simply drop the word infinite. There are cases where it is appropriate. What is the cardinality of the natural numbers? Infinite... "unbounded" is definitely not right there. But when we use infinity in proofs, we are more often using it to mean "unbounded" rather than truly a "manifested infinity", to use a sloppy phrase; we're using it to get rid of the nasty edge case, not because we expect a real implementation of whatever the proof is proving to actually require infinite RAM. Also, by "we", I should clarify I mean discrete mathematicians and computer scientists, who are usually dealing in the discrete case. In the continuous case, infinities come up "for real" more often.