> On 3 Mar 2019, at 22:58, Brent Meeker <meeke...@verizon.net> wrote: > > > > On 3/3/2019 1:37 PM, John Clark wrote: >> On Sun, Mar 3, 2019 at 2:52 PM Philip Thrift <cloudver...@gmail.com >> <mailto:cloudver...@gmail.com>> wrote: >> >> > If a program "represents" a real number (e.g. in the spigot sense), then >> > that could be said to "define" it. >> >> But for most Real Numbers there is no such program. >> >> > But what does it mean for a real number to be "defined"? >> >> If you can point to a property that a Real Number has that no other Real >> number does then it is defined; > > The smallest real number that is not defined.
That is a version of Berry Paradox. Chaitin used it to give a proof of its incompleteness theorem (proved a long time before by Post). It means that we do not have an all encompassing notion of “definable”, a bit like Truth. We can, nevertheless, define it for large class of objects. So, here, “the smallest non definable real number” does not define a number. Bruno > > Brent > >> a number like PI can be defined and you can approximated it with a >> calculation, a Busy Beaver Number can be defined but not approximated, most >> Real Numbers can not be defined or approximated and thus most Real Numbers >> can not be named. >> >> John K Clark >> >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to everything-list+unsubscr...@googlegroups.com >> <mailto:everything-list+unsubscr...@googlegroups.com>. >> To post to this group, send email to everything-list@googlegroups.com >> <mailto:everything-list@googlegroups.com>. >> Visit this group at https://groups.google.com/group/everything-list >> <https://groups.google.com/group/everything-list>. >> For more options, visit https://groups.google.com/d/optout >> <https://groups.google.com/d/optout>. > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
