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Topic: Warning to visitors to sci.math
Replies: 266   Last Post: Mar 19, 2012 9:13 AM

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 ross.finlayson@gmail.com Posts: 2,714 Registered: 2/15/09
Re: Warning to visitors to sci.math
Posted: Mar 17, 2012 10:36 AM

On Mar 16, 12:34 am, "Ross A. Finlayson" <ross.finlay...@gmail.com>
wrote:
> On Mar 15, 11:57 pm, "DavidW" <n...@email.provided> wrote:
>
>
>
>
>

> > Rotwang wrote:
> > > On 16/03/2012 03:43, DavidW wrote:
> > >> Rotwang wrote:
> > >>> On 16/03/2012 02:52, DavidW wrote:
> > >>>> [...]
>
> > >>>> Did you need to use infinite sets or only induction?
>
> > >>> Infinite sets, specifically the sets s_n, as well as {lub s_n | n in
> > >>> N} and {glb s_n | n in N}. Induction doesn't come into that part at
> > >>> all and I don't see how it could

>
> > >> I'll go away and have a closer look at your proof and stop bugging
> > >> sci.math with this for the moment. But before looking at it my
> > >> thinking is that infinite sets, including your s_n etc. are defined
> > >> by induction.

>
> > > I don't know what that could mean.
>
> > I just mean that you can define each term in a series from the application of
> > some rule to preceding terms. Maybe induction is too narrow. You can generate
> > the terms according to some rule, so by knowing the rule maybe you can make
> > deductions without requiring "all" of the infinite set.

>
> > >> The question is whether you
> > >> need "all" elements of those sets at any stage to make the proof
> > >> work, or if you only need to prove that particular properties hold
> > >> for each successive element in them. I would be troubled if you
> > >> really need "all" of an infinite set, because I consider that a
> > >> contradiction in terms.

>
> > > Well, you could change the real number axioms by replacing the
> > > completeness axiom with an axiom that states that every Cauchy
> > > sequence has a limit (which can be proved to be equivalent to
> > > completeness if one uses infinite sets), for example - that would
> > > bypass the need for infinite sets in the proof I gave. But I don't
> > > see what you would gain from this, since I don't see why you think
> > > that the notion of an infinite set is any more problematic than that
> > > of an infinite sequence. You've said that one "cannot have _all_ of
> > > something that is unbounded". Why do you think that the existence of
> > > the set of natural numbers means having all of something unbounded,

>
> > No, my problem is _if_ you ever treat the set as though you have all of
> > something unbounded.

>
> > > but the existence of an infinite sequence (that is, a function whose
> > > domain is all of the natural numbers) doesn't? Is it just that the
> > > word "set" invokes the image of a container, and you don't accept the
> > > idea of something containing an infinite number of things? If so then
> > > just call them something other than sets, and use a word other than
> > > "in" for the elementhood relation. In practice, nothing that
> > > mathematicians use sets for actually depend on thinking of sets as
> > > "containing" things.

>
> > I'll have to digest all this along with your proof and your flags idea and then
> > think about my position.- Hide quoted text -

>
> > - Show quoted text -- Hide quoted text -
>
> > - Show quoted text -
>
> Why not just partition into ranges here?  In differenceing we know
> that is uniform.  It is because that another useful general purpose
> algorithm uses a flag on each item simply, instead of coding (which
> compresses but requires decompression to be laid out).  We can see it
> is both, there are generally purposeful algorithms on each.
>
> Here basically it is as simple as the consequences of coding the flags
> into ranges (in real space).  It is also of course then as complex.
>
> The kind of proof that Rotwang writes is utter dogma.  That is what
> we're talking about when is said "standard real analysis".  That, and
> 1 + 1 = 2.
>
> Rant on Leonard, yes or no?  I already have one.- Hide quoted text -
>
> - Show quoted text -

Hell objectively Transfer Principle's one of the few who's civil.

Christ you expect people who study mathematics and have presumably
thus spent some time in the classroom to appreciate balance in debate,
or at least protection of argument in debate. (Heh, depends on the
classroom.)

It's not like the mathematical world isn't totally interested in new
foundations. It's like the rabble complaining to Leonard, "your
challengers to ZF are insufficient to make us look different than
bitter."

I have enough books right here, I can spend the next fifty years just
writing them all out together. And it would make me rich. But,
what's the point of being the next monkey with a typewriter? There
aren't even any breaks all you can do is smoke. That and screech,
well generally however you go about typing as a monkey here it is
"infinite monkeys with typewriters". Monkey life is pretty good.

Then, in Leonard's zoo, he has all the theories in his zoo. (By now
Tony is another lion.) Or, not a zoo, but Leonard's colloquium of
sorts, so Wolfgang is this plain old professor. I'm there but they
took the sign off. Or how about "we're not quite sure what's in it".
Great. So in Leonard's zoo, basically there are lions but how many
cows is that to feed them. Then for infinite regress is the case of
the lions. Basically whether philosophers dine if they have a fork,
lions sleep or eat the nearest thing.

You know I have read some four-five hundred science fiction books
cover-cover? You do now. That was 20 years ago got no time for that.

What is this whining or whinging at who, Transfer Principle? Christ
you guys want bats with that? I think that is as they say "come at
me, bro".

http://www.math.ias.edu/sp/univalent/goals

If you're into ZF or ZFC why don't you get yourself some of that.

Leonard wants to cultivate his zoo, lions are good for what, eating,
so basically it is arena lions. Then I guess that's right here. Then
the rabble has run out of lions and turned on Leonard.

Leonard's looking for the lion that can't be tamed (that mathematics
doesn't eat).

Not my problem. I got your lion right here. It's pretty full.

But why, why would you post this when you know I have enough time to
set up?

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