Re: infinity

Jiri Lebl said:
> Jesse F. Hughes wrote:
> > "Jiri Lebl" <jirka@xxxxxx> writes:
> > > Jesse F. Hughes wrote:
> > >> (A z)(z < x => (E y)(y < z)).
> > >
> > > That's not true, Take N union {aleph_0} and order it normally.
> >
> > Quite right. I realized this after posting, but didn't fix it.
>
> I make mistakes like that all the time. My advisor just yesterday
> caught me doing a totally freshman algebra mistake (I messed up the
> distributive law, because I was so fixated on the result that I didn't
> check my work:)
Huh! Given your attitude I rather imagined you were older. Just a young 'un I
see. Maybe there's hope for you yet! Of course, eberyone makes mistakes.
>
> Anyway, I suppose everybody (except Don Knuth I've heard) makes
> mistakes, and unlike Tony those that have some functioning neurons,
> realize when they've messed up and admit it. Now there are two
> possibilities for Tony. Either he is a total idiot and has not
> realized he's wrong, or he's just immature and won't admit he's wrong.
Gee, since I have probably been thinking about this longer than you've been
alive, you might want to reserve judgement before calling people idiots, just
because they disagree with the mainstream. By the way, hard right conservatives
think I'm an idiot too, but I really can't be overly concerned with that.
>
> > Of course, the circularity is due to Tony's bleatings. He wants to
> > say that an infinite set must have elements that are infinite in size,
> > infinitely far apart, have infinitely many predecessors, etc. Maybe
> > he even thinks that's a definition. But the use of "infinite" in each
> > case is either undefined or refers again to set size.
>
> Every possible definition of infinite size I can think of which would
> involve having a linearly ordered subset with no end in effect. But
> Tony thinks that is finite.
Unbounded.
> Once you've put two ends on a set, and
> don't think that something which doesn't end is infinite. Then I can't
> see any possible definition for infinity.
Infinity essentially mean unending, and the Peano axioms define an infinite
set. But, that set has infinite elements in it, due to the 1-1 correspondence
between position and value for each element in the set.
>
> I think Tony's numbers have a sort of structure like
>
> {0,1,2,3,...} union {...,N-3,N-2,N-1,N}
{-oo, -oo+1, -oo+2.....-2, -1, 0, 1, 2.........oo-2, oo-1,oo}
One CAN cross the Twilight Zone with INFINITE increments.
>
> In that ordering. That is two copies of normal finite natural numbers
> pasted next to each other. Though obviously he thinks that these would
> be finite sets, so their union must be finite. Thus the set looks
> like:
>
> {0,1,2,3,...} union {"Twilight Zone"} union {...,N-3,N-2,N-1,N}
"Obviously"??? No. If your second set had only finite subtractions from N, it
would be finite, and the bottom end would have infinite values as well. See my
other post where I compare the interval [0,1] to the interval [1,oo]. The
finites, at the infinite scale, are all clustered at the point next to 1. Any
finite distance from that end of the line denotes an infinite value. So there
are infinitely more infinite values than finite ones. The twilight zone is the
point which is the largest finite number of points from 1, the mark between
nothing and something on that scale.
>
> Where the twilight zone makes the set infinite, but it is something you
> can't quite get at because if you could find and identify any number in
> it, you could prove contradictions.

You would define the largest finite and smallest infinite, which would indeed
produice contradictions.
> So you can't detect it in any set,
> so I assume you have to use some supernatural powers to "feel" the
> infiniteness of the set.

Uh, yeah, the force, or whatever. (sigh)
> Somehow the twilight zone must contain most
> of the elements of the set, but no matter what operations you do you
> can never land there other wise you would get some concrete numbers in
> the twilight zone.
The twilight zone doesn't contain any elements. The largest finite natural is
like the smallest finite real. It can't be determined.
>
> Of course there are other contradiction from this as for example you
> will NEVER get out of the first set by just adding 1 so you never get
> to the twilight zone and so most definitely you never emerge on the
> other end.
The moment you touched the Twilight Zone, you would already be on the other
side. You cannot get to the other side in any finite number of finite steps.
You need an infinite number of steps, or infinite-size steps, to achieve
infinity.
>
> Jiri
>
>

--
Smiles,

Tony
.

Relevant Pages

  • Re: Orlow cardinality question
    ... >> means finite strings, I think - things with a left end and a right end ... infinite sequences of characters from an alphabet (conventionally ... > all sets of finite reals is bigger than the set of all finite reals, ... Numbers get bigger and bigger, approach the twilight zone, ...
    (sci.math)
  • Re: infinity
    ... >> Tony Orlow wrote: ... as an infinite natural number. ... Of course Tony denies that adding one to a finite ... it may well be that the twilight zone is halfway between 0 ...
    (sci.math)
  • Re: Orlow cardinality question
    ... >>> the set of strings over my set includes ... > infinite sequences of characters from an alphabet (conventionally ... >> all sets of finite reals is bigger than the set of all finite reals, ... Numbers get bigger and bigger, approach the twilight zone, ...
    (sci.math)
  • Re: Cantor and the binary tree
    ... Tony Orlow wrote: ... >>> is, and if one is infinite, so is the other. ... I notice that Dik said "paths" rather than branches. ... I presume you have passed through the twilight zone, ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... To be honest I'm impressed with Tony. ... > Virgil basically attacks Tony, and as above tries to segregate him. ... I think Virgil has a very vested interest in the standard model. ... "uuncountably" infinite set, without the kind of discontinuities we find in the ...
    (sci.math)
Quantcast