Another Alternative
Another axiom which implies the axiom of pairing in the presence of the axiom of empty set is
- .
Using {} for A and x for B, we get {x} for C. Then use {x} for A and y for B, getting {x,y} for C. One may continue in this fashion to build up any finite set. And this could be used to generate all hereditarily finite sets without using the axiom of union.
Read more about this topic: Axiom Of Pairing
Famous quotes containing the word alternative:
“If you have abandoned one faith, do not abandon all faith. There is always an alternative to the faith we lose. Or is it the same faith under another mask?”
—Graham Greene (1904–1991)
“Our mother gives us our earliest lessons in love—and its partner, hate. Our father—our “second other”Melaborates on them. Offering us an alternative to the mother-baby relationship . . . presenting a masculine model which can supplement and contrast with the feminine. And providing us with further and perhaps quite different meanings of lovable and loving and being loved.”
—Judith Viorst (20th century)