Sandy
Posts:
40
Registered:
7/9/13


Re: Effective method of getting a onetoone onto function from a onetoone function?
Posted:
Sep 15, 2013 8:23 AM


William Elliot wrote: > On Fri, 13 Sep 2013, Sandy wrote: > >> Suppose X is a set with aleph_0 members and f:X>N is a onetoone function. >> Is there an effective (maybe even "canonical") method of defining g:X>N in >> terms of f so that g is onetoone and onto? > > Carefully check this. > > Let [n,m] = [n,m] /\ N. > > Set s1 = min{ n : 0 < f^1([1,n]) }, > s_(k+1) = min{ n : sk < f^1([1,n]) }. > > (sk)_k is an increasing sequence into N. > > Let g(x) = min{ k  f(x) in [1,sk] }.
Thank you. I shall look into it.

