Re: infinity
- From: Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx>
- Date: Tue, 06 Sep 2005 15:58:35 -0600
In article <MPG.1d87a0e088436e2d98a1e6@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> Jiri Lebl said:
> > ...snip...
> > > > >> [1] For all s a string, exists L a length s.t. L > len(s)
> > > > >>
> > > > >> [2] Exists L a length s.t. for all s a string, L > len(s)
> > ...snip...
> > > > So are you saying that [2] means the same thing as [1], even
> > > > though the quantifiers are reversed?
> > ...snip...
> >
> > aeo6 Tony Orlow wrote:
> > > No, I am saying that [1] implies [2].
> >
> > So you think that [2] does not imply [1]?
> >
> > Jiri
> >
> >
> Certainly [2] implies [1]. I don't care to argue the equivalence of
> these two statements. Logically, they are different. I understand
> there is no largest finite, so [2] seems to contradict that, so I'll
> concede this little point. My original intention, however, was to
> show that some string must be infinite, because ANY finite value for
> a maximum string length yields a finite language. If there are ONLY
> finite string lengths, then there can ONLY be finite languages.
TO just blew it again, his conclusion here assumes [2] but [2] is false
for the set of lengths being the set of finite naturals.
.
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