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)
“A mental disease has swept the planet: banalization.... Presented with the alternative of love or a garbage disposal unit, young people of all countries have chosen the garbage disposal unit.”
—Ivan Chtcheglov (b. 1934)