what is ordered set?

Question

real numbers in real analysis

Answer 1

en.wikipedia.org/wiki/Partially_ordered_set

Please chick on the above URL for additional information.

Answer 2

An ordered set is any set together with a binary relation, a notion of "this element is bigger than this element."

An example: The real numbers with the relation less-than-or-equal-to define a totally ordered set. It is clear that of any two numbers you can say "this one is bigger than this one."

A partially ordered set is a set, with a binary relation, such that not every pair of elements in the set are related.

An example: Take the set of all subsets of the natural numbers, with the ordering is-a-subset-of. Then {1,2,3} is a subset of {1,2,3,4} so loosely "{1,2,3,4} is bigger than {1,2,3}", however consider {1,2,3} and {5,6,7} - neither of which is a subset of the other. In a partial ordering, only some pairs of elements are ordered.

Answer 3

For all a,b elements of R (the set of real numbers), ab.

Answer 4

any set together with a binary relation, a notion of "this element is bigger than this element."

Answer 5

http://en.wikipedia.org/wiki/Total_order#Examples

Answer 6

{1,2,3,4,5}