Re: Small Set Theory,Updated.



zuhair wrote:
As an example to see what I mean: take for example the empty set { } ,
i.e the set which has no member in it. now using the formula x is
P_defined were P is any Predicate that does't use x.we can define { }
by two predicates .

i) P[y]<-> ~y=y.
ii) P[y]<->(Az(~zey)).

That's already mixed up.

~y=y
states the condition for y being a MEMBER of the empty set.

Az~zey
states the condition for y BEING the empty set.

MoeBlee

.



Relevant Pages

  • Re: Small Set Theory,Updated.
    ... MoeBlee wrote: ... P_defined were P is any Predicate that does't use x.we can define ... states the condition for y being a MEMBER of the empty set. ...
    (sci.math)
  • Re: A theory with two axiom schemes in which ZF is interpreted as a subtheory of it.
    ... On Tue, 21 Jul 2009, zuhair wrote: ... for example 0 is a defined constant denoting the empty set. ... That's not a constant symbol, it's a one place predicate. ...
    (sci.logic)
  • Re: Is {} and element of all sets?
    ... empty set can be a member of other sets, ... The empty set is a member of } using the common interpretation. ... and where "element of" means being either a primitive element within ...
    (sci.math)
  • Re: Is {} and element of all sets?
    ... Nobody believes that the set theory you learned in high school had ... to distinguish between membership and being an elementary member. ... The question was whether the empty set is an element of every set. ... "Is there some inconsistency between common interpretations of ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... with it is power set, and with it the identity mapping of the power ... The existence of an empty set does ... member of the universe of every model of ZFC? ...
    (sci.math)