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)
“It provokes the desire but it takes away the performance. Therefore much drink may be said to be an equivocator with lechery: it makes him and it mars him; it sets him on and it takes him off.”
—William Shakespeare (1564–1616)
“No real “vital” character in fiction is altogether a conscious construction of the author. On the contrary, it may be a sort of parasitic growth upon the author’s personality, developing by internal necessity as much as by external addition.”
—T.S. (Thomas Stearns)