An uncountable countable set
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From: MoeBlee on 21 Sep 2006 13:13 Virgil wrote: > In article <45119c60$1(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > > > MoeBlee wrote: > > > Tony Orlow wrote: > > >>> It isn't. What does "successor to N" even mean? > > >> Ask von Neumann. It is the set of all naturals, > > > > > > What are you talking about? The successor of w is not w. The successor > > > of w is wu{w}. > > > > The size of the set x is the value > What "value" > > > > and it contains every natural less > > than x. > Cardinalities, as cardianlities, do not contain anything. The cardinality of a set is a set, so except for 0, the cardinality of a set has members. MoeBlee
From: MoeBlee on 21 Sep 2006 13:17 Tony Orlow wrote: > Because N is defined as including all finite naturals, it is potentially > infinite, each element having a finite index in the set. I suppose you mean T-potentially infinite. But do you mean set theoretic N or T-N? MoeBlee
From: MoeBlee on 21 Sep 2006 13:20 MoeBlee wrote: > Tony Orlow wrote: > > Because N is defined as including all finite naturals, it is potentially > > infinite, each element having a finite index in the set. > > I suppose you mean T-potentially infinite. But do you mean set > theoretic N or T-N? P.S. If you mean set theoretic N, then it depends on which treatment we are using whether N is defined as you described or whether instead it is a theorem that N is as you described. MoeBlee
From: MoeBlee on 21 Sep 2006 13:20 MoeBlee wrote: > Tony Orlow wrote: > > Because N is defined as including all finite naturals, it is potentially > > infinite, each element having a finite index in the set. > > I suppose you mean T-potentially infinite. But do you mean set > theoretic N or T-N? P.S. If you mean set theoretic N, then it depends on which treatment we are using whether N is defined as you described or whether instead it is a theorem that N is as you described. MoeBlee
From: Virgil on 21 Sep 2006 14:14
In article <73452$45123e3f$82a1e228$7325(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <3a6c6$4510f00a$82a1e228$27505(a)news2.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > >>David R Tribble wrote: > >> > >>>mueckenh wrote: > >>> > >>>>>Nothing has changed. There is no complete set of natural numbers. Any > >>>>>set that can be established is a finite set. Hence, the probability to > >>>>>select a number divisible by 3 is 1/3 or very very close to 1/3. > >>> > >>>Virgil wrote: > >>> > >>>>That presumes that the allegedly finite set of naturals that can be > >>>>constructed is nearly uniform with respect to divisibility by 3 at > >>>>least, and probably by other numbers as well. What is the justification > >>>>for this assumption? > >> > >>Wolfgang says litteraly: "_or_ very very close to 1/3". > > > > Which requires "_nearly uniform_ with respect to divisibility by 3". > > Sorry, Virgil. I don't get it. As usual. |