History of TotalOrderedSet

	Revision 6 . . January 29, 2001 9:31 am by RoseParks
	Revision 5 . . (edit) January 29, 2001 6:50 am by JoshuaGrosse
	Revision 4 . . (edit) January 29, 2001 6:49 am by JoshuaGrosse
	Revision 3 . . (edit) January 29, 2001 6:47 am by JoshuaGrosse
	Revision 2 . . (edit) January 26, 2001 4:20 pm by JoshuaGrosse
	Revision 1 . . January 23, 2001 6:29 pm by JoshuaGrosse

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Difference (from prior major revision) (no other diffs)

Changed: 1c1

A total-ordered set is a LatticE (T,v,^) where for any a,b in T, either avb=a and a^b=b, or avb=b and a^b=a. A PartialOrder <= on a set T defines a total order if and only for every a,b in T, exactly one of the following hold:

A total-ordered SeT is a LatticE (T,v,^) where for any a,b in T, either avb=a and a^b=b, or avb=b and a^b=a. A PartialOrder <= on a set T defines a total order if and only for every a,b in T, exactly one of the following hold:

Changed: 9c9

The unique smallest total-ordered set with neither an upper nor lower bound is the IntegerNumbers. The unique smallest unbounded total-ordered set which also happens to be dense, that is have non-empty (a,b) for every a<b, is the RationalNumbers. The unique smallest unbounded connected total-ordered set is the RealNumbers?.

The unique smallest total-ordered set with neither an upper nor lower bound is the IntegerNumbers. The unique smallest unbounded total-ordered set which also happens to be dense, that is have non-empty (a,b) for every a<b, is the RationalNumbers. The unique smallest unbounded connected total-ordered set is the RealNumbers?.