Re: Proper classes


David R Tribble wrote:
> Zuhair wrote:
> >> why cardinality is a property of sets and not a property
> >> of proper classes?
> >
>
> Jonathan Hoyle wrote:
> >> Because proper classes are not defined to have that property. It is
> >> the same answer as to the question: "Why is cardinality is a property
> >> of sets and not a property of ketchup?"
> >
>
> Zuhair wrote:
> > Jonathan all of your answers are empty , most of them are circular , I
> > have pritty good experience with your answers . You say they are not
> > defined to have that property as if it is a matter of definition. Fair enough
> > still the same question exists:
> > Why they are not defined to have that property.
> >
> > Cardinality is a measure of the multiplicity of terms or members, anything which
> > has members should have cardinality , proper classes has members why
> > should they dont have cardinality.
>
> I have a class C2 of all the sets containing two elements.
> What is the cardinality of C2?
>
> I have another class C3 of all the sets containing three elements.
> What is the cardinality of C3? Is class C2 bigger than C3?

No C2 is smaller than C3, see Bertrand Russell's definition of Number.

The cardinality of C2 is 2 the cardinality of C3 is 3.

Zuhair

.

Relevant Pages

  • Re: Proper classes
    ... Cardinality can be applied to sets, ... > correspondence is not defined on proper classes, ... >>> members, anything which has members should have ... > In NBG Set Theory, you can define a bijection on proper classes! ...
    (sci.math)
  • Re: Proper classes
    ... > zuhair wrote: ... >>Why sets has cardinality, while proper classes doesn't. ... > corresponding to injections and bijections. ...
    (sci.math)
  • Re: Question about Cardinality and Proper Classes
    ... > and proper classes is that proper classes are "too large" to be ... > and proved in ZFC. ... now just gives us exactly one of the members of F). ... Uof C_Phi must have a cardinality of at least k'. ...
    (sci.logic)
  • Re: Proper classes
    ... Zuhair wrote: ... >> why cardinality is a property of sets and not a property ... Jonathan Hoyle wrote: ... >> Because proper classes are not defined to have that property. ...
    (sci.math)
  • Re: Proper classes
    ... Zuhair wrote: ... >> why cardinality is a property of sets and not a property ... Jonathan Hoyle wrote: ... >> Because proper classes are not defined to have that property. ...
    (sci.math)