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:
“The stately Homes of England,
How beautiful they stand,
To prove the upper classes
Have still the upper hand.”
—Noël Coward (1899–1973)
“I must have the gentleman to haul and draw with the mariner, and the mariner with the gentleman.... I would know him, that would refuse to set his hand to a rope, but I know there is not any such here.”
—Francis, Sir Drake (1540–1596)