Re: fastest way to print a lot of pdf files?

Erik Max Francis <max@xxxxxxxxxxx> wrote:
> Peter T. Breuer wrote:

>> In all versions of mathematics, cardinality means the existence of a
>> bijection. The trick is in "what is a function" (a bijection). If,
>> within a classic system of mathematics like the one you have in mind,
>> you imagine a "flatlander" who only believes in functions that
>> correspond to a computational procedure, you get a model for another
>> (relatively consistent) version of mathematics (hey, but we know it is
>> consistent, because it has a model), called "constructivism".

> This wasn't your objection earlier; your objection earlier was that
> there wasn't enough _time_ to enumerate all the possibilities.

No - I pointed to the situation where new pdf's were being made quicker
than they could be counted. That's TOO MUCH time, not NOT ENOUGH time.

> That
> indicates you don't know what cardinality means,

Yes I do.

> because cardinality has
> nothing to do with an actual enumeration of all possible instances of a
> set

Yes it does, because in in my belief system (for the sake of argument)
all functions are procedures. I simply don't believe in the exisence of
functions that aren't procedures and you can't make me, nernerner.

(That's a perfectly self-consistent belief called "constructivism", and
it's relatively consistent to the classical view too - amusingly, a
classicist can actually prove that in a minimal model for such a
costructivist system, the axiomm of choice holds; I don't think the
proof is available to constructivists however, hmmm, but it might be
....).

> in some finite amount of time.

NO I didn't! Stop inventing absurdities! What is this? I say something
perfectly normal and self-evident and people invent all sorts of weird
and strange and FALSE interpretations of my perfectly ordinary words.

[rest snipped in exasperation]

> It's trivially easy to create a bijection between an arbitrary length
> array of a finite set of symbols and the integers.

Well, that's not true either! It's not easy. Ask a sysadmin. Google has
that problem. They have to count how many DISTINCT queries there are in
a year - the trouble is, the logs of those queries are scatered on each
of their logging machines (say 120).

Now tell me how they create that bijection of yours- indeed, we're lucky
they do it "per year", because if it were a running count they couldn't
keep up.


> Now you're talking about the axiom of choice, which only applies to
> infinite sets here,

That's because you are the only person thinking I am talking about a
finite set! I'm not. But then you are also wrong about the finitist
view.

Peter
.

Relevant Pages

  • Re: Epistemology 201: The Science of Science
    ... :>: be preferred in mathematics or science simply because it is more ... :>:> implications of cardinality. ... definition of number of elements that gave rise to the bijection approach ... The "size" of the sets of octal and decimal strings remain the same ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... :>: be preferred in mathematics or science simply because it is more ... :>:> implications of cardinality. ... definition of number of elements that gave rise to the bijection approach ... The "size" of the sets of octal and decimal strings remain the same ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... :>: be preferred in mathematics or science simply because it is more ... :>:> implications of cardinality. ... definition of number of elements that gave rise to the bijection approach ... The "size" of the sets of octal and decimal strings remain the same ...
    (sci.physics)
  • Re: abundance of irrationals!)
    ... >>> does not state anything about the cardinality of the set. ... >>> for any finite set, because we dobt the existence of infinite sets. ... >> existence of red apples. ... > 2) or you can specify any n e N for which my bijection is undefined. ...
    (sci.math)
  • Re: bijection of R: R <--> Rx.....xR
    ... If there exists a bijection between 2 infinite ... But these sets do have the same cardinality. ... sets ignores most of the useful distinctions of mathematics. ...
    (sci.math)