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:
“But that beginning was wiped out in fear
The day I swung suspended with the grapes,
And was come after like Eurydice
And brought down safely from the upper regions;
And the life I live now’s an extra life
I can waste as I please on whom I please.”
—Robert Frost (1874–1963)
“It is a great mistake to suppose that clever, imaginative children ... should content themselves with the empty nonsense which is so often set before them under the name of Children’s Tales. They want something much better; and it is surprising how much they see and appreciate which escapes a good, honest, well- informed papa.”
—E.T.A.W. (Ernst Theodor Amadeus Wilhelm)