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:
“If the upper beams are not straight, the lower beams will be crooked.”
—Chinese proverb.
“They smote and fell, who set the bars
Against the progress of the stars,
And stayed the march of Motherland!”
—Will Henry Thompson (1848–1918)