In mathematics, an upper set (also called an upward closed set or just an upset) of a partially ordered set (X,≤) is a subset U with the property that, if x is in U and x≤y, then y is in U.
The dual notion is lower set (alternatively, down set, decreasing set, initial segment; the set is downward closed), which is a subset L with the property that, if x is in L and y≤x, then y is in L.
Read more about Upper Set: Properties, Ordinal Numbers
Famous quotes containing the words upper and/or set:
““All men live in suffering
I know as few can know,
Whether they take the upper road
Or stay content on the low....””
—William Butler Yeats (1865–1939)
“One of the main tasks of adolescence is to achieve an identity—not necessarily a knowledge of who we are, but a clarification of the range of what we might become, a set of self-references by which we can make sense of our responses, and justify our decisions and goals.”
—Terri Apter (20th century)