Partially ordered set, totally ordered set, totally ordered set, and well ordere
ID: 3649872 • Letter: P
Question
Partially ordered set, totally ordered set, totally ordered set, and well ordered set form a hierarchy, in that each catagory is more restrictive than the ones that come before it. For each of the following decide if the set with the relation is not partially ordered, partially ordered but not totally ordered, totally ordered but not well ordered , or well ordered.a. "is ancestor of" on the set of people, where a person is considred to be an ancestor of him- or herself
b. "is parent of" on the set of people
c. "is divisible by" on the set of positive integers
d. less than or equal to on the set of numbers that can be expressed as a positive integer divided by 1, 2,or 3
e. less than or equal to on the rational numbers r with 1 less than or equal to r less than or equal to 2
f. less than or equal ton on any finite subset of the rational numbers.
Explanation / Answer
In mathematics, especially order theory, a partially ordered set (or poset) ... Such a relation is called a partial order to reflect the fact that not every pair of ... Thus, partial orders generalize the more familiar total orders, in which every pair is related. ... by the standard less-than-or-equal relation = (a totally ordered set as well).