Re: infinity


Tony Orlow (aeo6) wrote:
> stephen@xxxxxxxxxx said:
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > > stephen@xxxxxxxxxx said:
> > >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > >> > stephen@xxxxxxxxxx said:
> > >> >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > >> >> > stephen@xxxxxxxxxx said:
> > >> >> >> I am not assuming that there is a longest word. A longest word
> > >> >> >> implies a largest natural number. You always deny that there
> > >> >> >> is a largest natural number, but once again you are using an
> > >> >> >> argument that depends on there being a largest natural number.
> > >> >> > I said "longest WORDS", not "longest word".
> > >> >>
> > >> >> There are no longest words either, so I am not assuming
> > >> >> anything about them. There is no maximum finite word length.
> > >> >>
> > >> >> >>
> > >> >> >> I have no idea what L is in your S^L. You are aware that there
> > >> >> >> is more than one string length, so picking a single L does not
> > >> >> >> make any sense. It almost makes sense if you think that L is
> > >> >> >> the maximum string length, i.e. the largest finite natural number.
> > >> >> >> Of course you also deny that there is a maximum string
> > >> >> >> length, so I have no idea what S^L is supposed to mean.
> > >> >> > Given any string length and alphabet, that is the maximum number of unique
> > >> >> > srings in the language.
> > >> >>
> > >> >> I asked what L is. L is not the maximum number of unique
> > >> >> strings in the language.
> > >> > You said you had no idea what S^L is, even though we have discussed this
> > >> > before. L is any string length as I said. What do you not understand?
> > >>
> > >> Again, I do not understand what L is. Is L the length of any
> > >> string? Well, then lets look at the language of strings on
> > >> the alphabet {0,1} of length 100 or less. Is the size of this
> > >> language 2^55? 55 afterall is a length less than 100. Or is the size of
> > >> the language 2^23? What is the value of L I should plug into
> > >> 2^L to determine the size of this language?
> > > All of them up to 100.
> > > sum(x=0->100: 2^x)
> >
> > So when I plug in all the finite L, I get an infinite
> > sum of finite values, i.e.
> > sum (x>=0 : 2^x)
> > Note, I did not plug in a single value of L like you
> > kept insisting. There are an infinite number of finite values
> > for x.
> No, I have shown that there are only a finite number of finite whole numbers.
> Your insistence that there are an infinite number of finite strings is a
> consequence of believing that there are an infinite number of finite naturals,
> which there are not.
> >
> >
> > >> >> There are an infinite number of finite k.
> > >> >> You cannot assume there are only a finite number of finite
> > >> >> k when trying to prove that there are only a finite number
> > >> >> of finite k.
> > >>
> > >> > Well, I have proven, at least to my own staisfaction, that you cannot have an
> > >> > infinite set of finite whole numbers, so when you say "finite k", I say you are
> > >> > counting a finite number of times and summing a finite number of terms, each of
> > >> > which is finite. You say I cannot assume that there are a finite number of
> > >> > finite naturals in trying to prove that there are a finite number of finite
> > >> > strings on a finite alphabet.
> > >>
> > >> You cannot assume what you are trying to prove.
> > > I didn't. You did.
> >
> > Very mature response. Your entire S^L proof that there
> > are only a finite number of values for L is based entirely
> > on the assumption again that there are only a finite number
> > of values for L.
> Which is proven elsewhere. Did you read my induictive proof that any set of
> naturals up to and including n has n not only as its largest element, but also
> as its set size?


And since the set of finite naturals is not a set of naturals up
to and including n, this trivial fact is of little interest.

-William Hughes

.

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