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

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