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?