On Jul 6, 11:26 am, MoeBlee <jazzm...@hotmail.com> wrote: > On Jul 6, 10:32 am, "Ross A. Finlayson" <ross.finlay...@gmail.com> > wrote: > > > On Jul 6, 9:20 am, MoeBlee <jazzm...@hotmail.com> wrote: > > > > On Jul 2, 6:00 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com> > > > wrote: > > > > > Here a choice function is a bijective function from an ordinal (which > > > > is a collection of all lesser ordinals) to a set, or vice versa. > > > > What does "here" refer to in your sentence? Choice functions are not > > > necessarily bijections, nor do they necessarily involve ordinals, so I > > > don't know what you're talking about. > > That's a well-ordering. > > WHAT is a well ordering? The "here" in your previous comments refers > to well ordering? > > > (Also in a theory where the well-ordering > > principle is axiomatized or a theorem it's an equivalent definition > > under minimization of terms.) > > What is equivalent to what? What are you talking about? > > > I think the definition of choice > > function includes that the range contains each element, > > What "each" element? > > If you mean that the definition of 'choice function on x' entails that > every member of x is in the range of the choice function, then you're > mistaken. > > > so it's a > > surjection onto the set. > > Every function is a surjection onto its range. So what? > > You're a pit of wasted time. > > MoeBlee
So, not every function is a surjection onto its co-image or range. That gets into definitions of "range", in classical, modern, standard, and as well modern nonstandard definitions of function.