Internal Sets in The Ultrapower Construction
Relative to the ultrapower construction of the hyperreal numbers as equivalence classes of sequences, an internal subset of *R is one defined by a sequence of real sets, where a hyperreal is said to belong to the set if and only if the set of indices n such that, is a member of the ultrafilter used in the construction of *R.
More generally, an internal entity is a member of the natural extension of a real entity. Thus, every element of *R is internal; a subset of *R is internal if and only if it is a member of the natural extension of the power set of R; etc.
Read more about this topic: Internal Set
Famous quotes containing the words internal, sets and/or construction:
“I maintain that I have been a Negro three times—a Negro baby, a Negro girl and a Negro woman. Still, if you have received no clear cut impression of what the Negro in America is like, then you are in the same place with me. There is no The Negro here. Our lives are so diversified, internal attitudes so varied, appearances and capabilities so different, that there is no possible classification so catholic that it will cover us all, except My people! My people!”
—Zora Neale Hurston (1891–1960)
“Almsgiving tends to perpetuate poverty; aid does away with it once and for all. Almsgiving leaves a man just where he was before. Aid restores him to society as an individual worthy of all respect and not as a man with a grievance. Almsgiving is the generosity of the rich; social aid levels up social inequalities. Charity separates the rich from the poor; aid raises the needy and sets him on the same level with the rich.”
—Eva Perón (1919–1952)
“Striving toward a goal puts a more pleasing construction on our advance toward death.”
—Mason Cooley (b. 1927)