Mathematically it roughly works like the following:

Let A be the collection of all sets. Let f be a map f:A->A a: |-> a U {a} Assign label '0' to Emptyset If a has label 'x' then assign label 'x+1' to f[a] Label a f[a] a U {a} --------------------- 0 Empty 1 f[Empty] Empty U {Empty} = {Empty} = {0} 2 {0} f[{0}] {0} U {{0}} = {0, {0}} = {0, 1} 3 {0,1} f[{0,1}] {0,1} U {{0,1}} ={0,1,{0,1}} ={0,1,2}

More later. ( Confirmed as an article in the NT Wiki. )

Is A a member of itself?

ReplyDeleteYes.

ReplyDeleteSee, http://web.mat.bham.ac.uk/R.W.Kaye/seqser/constructions

for my source.