> Date: Thu, 29 Nov 2007 18:25:54 +0100
> Subject: Re: Theory of Everything based on E8 by Garrett Lisi
> 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.

Why is that? How do you define the word "set"? 

  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.

Why can't I say "the set of all numbers which can be generated by that 
production ruler"? It almost makes sense to say a set is *nothing more* than a 
criterion for deciding whether something is a member of not, although you would 
need to refine this definition to deal with problems like Russell's "set of all 
sets that are not members of themselves" (which could be translated as the 
criterion, 'any criterion which does not match its own criterion'--I suppose 
the problem is that this criterion is not sufficiently well-defined to decide 
whether it matches its own criterion or not).

>>> 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.

Is there something intrinsic to your concept of the word "set" that makes this 
true? Is your concept of a set fundamentally different than my concept of 
well-defined criteria for deciding if any given object is a member or not?

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