
Re: Trichotomy of Cardinals
Posted:
Jul 4, 2014 5:33 PM


On 7/4/2014 2:25 PM, Aatu Koskensilta wrote: > "Ross A. Finlayson" <ross.finlayson@gmail.com> writes: > >> On 7/4/2014 12:06 PM, Aatu Koskensilta wrote: >>> William Elliot <marsh@panix.com> writes: >>> >>>> How is the trichotomy of cardinals equivalent to AxC? >>> >>> In the form that says that given any two sets A and B, either A and B >>> are equipollent; A and B are not equipollent but A is equipollent to a >>> subset of B; or A and B are not equipollent but B is equipollent to a >>> subset of A. >>> >>>> Defining the cardinals as done within ZF, as the the initial ordinals, >>>> aren't they well ordered? >>> >>> Sure. >>> >>>> Thusly a proof for AxC? >>> >>> Observing that a class of ordinals is wellordered falls somewhat >>> short of a proof of the axiom of choice. >>> >> >> 2 <> 3 > > This is no doubt a pertinent observation, if somewhat obscure. >
2 <> 3, yes these are the numbers, why 2 and 3 are so, here in trichotomy where there is otherwise only dichotomy, for example.
Why yes it is.
Mathematics is so advanced, we're figuring out 2 and 3.
Really this is the 21'st century mathematics.

