Re: infinity
- From: imaginatorium@xxxxxxxxxxxxx
- Date: 14 Oct 2005 23:48:39 -0700
William Hughes wrote (about sets with no largest value):
> Tony Orlow wrote:
> > William Hughes said:
<megasnip>
> > > Please recite 100 times before bed:
> > >
> > > Some sets do not have a largest value.
> > One can speak of infinite sets UP TO any arbitrary value.
Ah! How more specfic could one get. Tony's "infinite" goes just so far,
just arbitrarily, imponderably, "infinitely" far...
> Yes some sets do have a largest value. However, this does
> not change the fact that some sets do not have a largest value.
>
> > This is the whole
> > point of declaring value ranges for comparison of such sets. The largest
> > natural I speak of exists in the context of the inductive proof that it is
> > equal to the set size for every n. It exists at every iteration of the proof,
> > through all of N.
>
> Actually it never exists. At each iteration of the proof you get
> a largest natural so far. However, you cannot combine all of these
> to get a single largest natural.
>
> Please recite 1000 times every morning.
>
> Some sets do not have a largest value.
Not likely. Tony does not grasp the idea of considering an unending
sequence. What you say ("no largest value") is true, of course, but
there is no set that does not have an "indefinitely good
approximation", for which there is indeed a largest value.
Brian Chandler
http://imaginatorium.org
.
- References:
- Re: infinity
- From: Tony Orlow
- Re: infinity
- From: Tony Orlow
- Re: infinity
- From: William Hughes
- Re: infinity
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