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:
“You doubt we read the stars on high,
Nathless we read your fortunes true;
The stars may hide in the upper sky,
But without glass we fathom you.”
—Ralph Waldo Emerson (1803–1882)
“Stories of law violations are weighed on a different set of scales in the Black mind than in the white. Petty crimes embarrass the community and many people wistfully wonder why Negroes don’t rob more banks, embezzle more funds and employ graft in the unions.... This ... appeals particularly to one who is unable to compete legally with his fellow citizens.”
—Maya Angelou (b. 1928)