Le Thursday 29 November 2007 18:25:54 Torgny Tholerus, vous avez écrit : > Quentin Anciaux skrev: > > Le Thursday 29 November 2007 17:22:59 Torgny Tholerus, vous avez écrit : > >> There is a difference between "unlimited" and "infinite". "Unlimited" > >> just says that it has no limit, but everything is still finite. If you > >> add something to a finite set, then the new set will always be finite. > >> It is not possible to create an infinite set. > > > > I'm sorry I don't get it... The set N as an infinite numbers of elements > > still every element in the set is finite. Maybe it is an english > > subtility that I'm not aware of... but in french I don't see a clear > > difference between "infini" and "illimité". > > As soon as you talk about "the set N", then you are making a "closure" > and making that set finite.

## Advertising

Ok then the set R is also finite ? > The only possible way to talk about > something without limit, such as natural numbers, is to give a > "production rule", so that you can produce as many of that type of > objects as you want. If you have a natural number n, then you can > "produce" a new number n+1, that is the successor of n. What is the production rules of the "no"set R ? > >> So it is OK to use the word "unlimited". But it is not OK to use the > >> word "infinite". Is this clear? > > > > No, I don't see how a set which have not limit get a finite number of > > elements. > > It is not possible for "a set" to have no limit. As soon as you > construct "a set", then that set will always have a limit. I don't get it. > Either you > have to accept that the set N is finite, or you must stop talking about > "the set N". It is enough to have a production rule for natural numbers. I don't accept and/or don't understand. > >> Another important word is the word "all". You can talk about "all > >> events". But in that case the number of events will be finite, and you > >> can then talk about "the last event". But you can't deduce any > >> contradiction from that, because that is forbidden by the type theory. > >> And there will be more events after "the last event", because the number > >> of events is "unlimited". > > > > If there are events after the last one, how can the last one be the last > > ? > > The last event is the last event in the set of "all" events. But > because you have a production rule for the events, it is always possible > to produce new events after the last event. But these events do not > belong to the set of "all" events. There exists no last element in the set N. > >> As soon as you use the word "all", you will > >> introduce a limit - all up to this limit. And you must then think of > >> only doing conclusions that are legal according to type theory. > > > > o_O... could you explain what is type theory ? > > Type theory is one of the solutions of Russel's paradox. You have a > hierarchy of "types". Type theory says that the "all quantifiers" only > can span objects of the same "type" (or lower types). When you create > new objects, such that "the set of all sets that do not belong to > themselves", then you will get an object of a higher "type", so that you > can not say anything about if this set belongs to itself or not. The > same thing with "the set of all sets". You can not say anything about > if it belongs to itself. > > >> So the best thing is to avoid the word "all" (and all synonyms of that > >> word). > > > > like everything ? > > Yes... :-) What you are saying seems like to me "So the best thing is to avoid words at all (and any languages)"... Regards, Quentin Anciaux -- All those moments will be lost in time, like tears in the rain. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---