Re: infinity

In article <MPG.1dc82ca33abe38a98a557@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> imaginatorium@xxxxxxxxxxxxx said:

> > There is no largest natural. You really are an idiot.

> Oh, then where in my enumeration of all the subsets shall I place the
> bit corresponding to my last element?

Stick it in the dark of TOmatics, where the sun don't shine, since
there is no "last" element anywhere else.

> > No. Because there is no largest natural, there is no such thing as
> > twice it. You really are an idiot.
> But the set is fixed, and has a fixed size, right? So, if there are N
> elements,

But N is not a number, so that there are not N elements.


> >
> > There is no last element. You
> > really are an idiot.

> I am certainly having a hard time getting my point across. From your
> perspective, that is probably the most palatable explanation.

As that "point" has no existence outside of TOmatics, TO should preach
his Gospel only to his choir, such as the likes of Zuhair and Ross.

Maybe start his own private NG for the faithful.

> >
> > Got that?

> You have some fixed set of naturals, right? Is there some fixed
> number of them?

There is a cardinality for the set of them, but nothing else.
> >
> > Since this is abstract mathematics, not junior computing, we are
> > not assigning "bits" to anything.

> That is precisely how my bijection works. Your dismissal of bits
> as"junior computing" do not wave away the bijection.

It waves away itself, at least outside TOmatics.

> >
> > Because cranks can't understand proper arguments, it's terribly
> > tempting to assume they might understand analogies. But it never
> > works like that.

> That all depends how much time you spend thinking up your analogies.
> That wasn't a very good one. Idiots don't get analogies anyway.

At least TO is right that TO does not get analogies, nor does TO get
valid proofs.

> > > But an infinite enumeration has no last element.
> >
> > Whoopee!! That's right, Tony. No last element. But we are still
> > considering the totality of all elements, none of them the last,
> > with no restrictions, no "value ranges", no "tenuous" or "variable"
> > not-the-last-element-but-let's-pretend.

> Yes the fixed set. So let's take the top 1/2 of it. What does it map
> to?

Show us the top half of {1,2,3}, or {1.2.3.4.5}. Not every finite set
has a "top half", so why should one expect infinite sets to have them?
> >
> > > Any properties of the set which depend on this being identified
> > > will run into problems.
> > Absolutely they will. Sometimes I feel hope for you, because unlike
> > most cranks, you can occasionally produce a sequence of more than
> > one correct sentence.
> Actually, I have an occasional wrong sentence. Nobody's perfect. But
> I'm not bad, despite your derisive comments.

It is your TOmatics that is bad, logically speaking, since it requires
mutually contradictory things to hold true.

> > There is no "top half" of the naturals. The naturals do not end -
> > it is an ever-so-slightly surprising result (to an average
> > intelligence) that there is no point "half-way" to the end, because
> > there is no end.
> Oh gee, and I thought the set was fixed and immutable, defined
> statically, based on its axioms, and with a certain size?

It is all of those things as a set, but as a sequence, it has no end.

> Is this the
> case, in your opinion, or not? Whatever the size is, why can't we
> talk about the first half of the ordered set and the second?

Because you are now talking about the sequence, not the set. The set,
purely as a set, has no order, it is entirely determned by what are its
members and what are non-members. The ordering applies only to the
sequence and the sequence does not have a first or second half.

If we
> can't talk about the top half, how can we talk about the size at all?

The sequence does not have a "size". The set has a cardinality, but need
not have a "size", since TO's notion of "size" requires existence of the
no-existent.
> >
> > Incidentally, people have said that (e.g.) the fact that the set of
> > naturals and the set of evens have the same cardinality is at odds
> > with ordinary intuition. Well, it's not part of ordinary
> > experience, but I do not think it is at odds with common sense,
> > actually. There's a joke I've heard (not a mathematicians' joke
> > either) in which some man is offered three wishes by a pixie. We
> > are supposed to giggle at his dimness, because for the first wish
> > he says:
> >
> > "I'll have an inexhaustible bottle of Guinness, please."
> >
> > And the pixie gives him this bottle, and sure enough, he drinks and
> > drinks and drinks, and the bottle is still full. Then for his
> > second wish he says:
> >
> > "Begorrah(*), I think I'll have another one of those..."
> >
> > (*) Yes I know.
> >
> > Anyway, the point is that whereas a crate of real Guinness can be
> > improved on by having two crates of real Guinness, an inexhaustible
> > bottle of Guinness (which is fictional, but essentially an infinite
> > amount of Guinness) cannot be improved on by having two of them.

> Oh, you mean, you can't fill your keg twice as quickly with two
> bottles, or pour twice as many glasses of beer per minute?

Precisely!

> Begorrah, what if I lose one?

Then someone else will find it.

>
> Seriously, though, if this is the case with *N, then how can you say
> P(*N) improves on this infinity? That seems to be at odds with what
> you just said here.

No one has said that 'larger' cardinality meant better.

And bijection , injection, and surjection only relate to cardinality,
not to any of TO's garbage sizing.
.

Relevant Pages

  • The Origin of a Sequence
    ... THE ORIGIN OF A SEQUENCE ... implications of the first part for the understanding of natural number as ... In mathematics, so far as I can tell, a sequence is always ... But let us go back to our idea of the Naturals ...
    (sci.math)
  • Re: Cantor Confusion
    ... But everyone says they make an adequate model for the naturals, ... If the sequence consists of segments of the form or, there ... is no segment which is diagonal in direction. ... I'm suggesting a definition of the curve as a sequence of pairs ...
    (sci.math)
  • Re: Dial 999 for the real number line
    ... the number of elements in a set is either infinite or it ... are an actually infinite set of naturals. ... You want to believe that even though the sequence of naturals is ... an infinite decimal expansion is ...
    (sci.math)
  • Re: Continuum hypothesis
    ... >>> your own set theory and discuss what is true in it, ... >> may be better things to work with, after all) Can you accept a sequence ... > just the same as the naturals? ... > uniform distribution on the naturals. ...
    (sci.math)
  • Re: Luann, August 27th
    ... This seems a bit like Roger Ebert's definition of "idiot plot". ... Would ANYONE, in real life, write numbers in this sequence? ...
    (rec.arts.comics.strips)
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