Re: Cantor For Dummies ...

No, you haven't defined precisely what your
list contains.

I don't have a list. But the collection of all
algorithms that output a committee can be listed.

Yes. The collection of all algorithms that output
a committee can be listed.

[My algorithm] does generate a committee.
I've said so repeatedly.

If you have a real algorithm and it outputs a
committee, then it's part of the collection.

Agreed.

However, it takes input to do so. You seem
either not to have noticed that, or to be
ignoring it.

That's not relevent.

I think it is. More about this below.

Since it's an important point I've been
trying to make that clear.

I realize that. You don't realize that the
collection of all algorithms that output a
committee is general enough to include them all.

I do realise that. I also realise that the specific
committee output by my algorithm depends on its input.
More about that below.

I claim that my process, when given a list of
committees, produces a committee. Do you agree?

If it is an actual algorithm and uses valid input.

Good. Agreed.

OK. So you want all algorithms whose output is
a committee, whether they require input or not.

Sounds good to me.

Good. Agreed.

... you want to talk about the output of
all these algorithms. Some of them, mine
included, don't produce output without
input. If you don't tell me what input
to use, we can't talk about the output.

I have no input to any algorithms. I'm
considering only their outputs.

Given that some of the algorithms, mine included,
require input before they produce output, how can
you talk about their output without talking about
their input? That sounds like nonsense to me, but
I'm sure it will become clearer below.

You can assume you have any valid input.
Use any valid input you desire. Note that
your algorithm's output is not valid to
use as its input.

So I'll take a single, fixed list of committees,
and I'll use that as the input for every algorithm
that requires a list of committees as input.

For some of them you can't list their output
without saying what their input is. So you
are wrong. We can't list their output.

YOU are wrong. I never said they would operate
without input.

No. You repeatedly ignored the question of what
input to give them. However, you've now said that
I can use any input I like, so I've chosen the input
I want. It's a single, fixed list of committees.

Assume whatever input you need. I have none. I
never claimed to have any input for your algorithm.
I only claim that if your algorithm uses ANY valid
input and generates a committee, then it's in the
list of algorithms that generate committees.

OK.

I suppose if we listed the outputs of all those
algorithms, ...

So on the one hand you say that you don't have
any input for the algorithms, and then on the
other hand you want to use their output. That
is inconsistent. However, we're moving on,
because you have let me use any input I like.

... we would have a list of committees.
But that list wouldn't be valid input for your
algorithm since part of that list would be your
algorithm's output.

That's fine, because my algorithm never uses that
output list. I never said my algorithm was supposed
to use the list of committees that the list of
algorithms produces. I never talked at all about
using the output as input.


Suppose you take your list of algorithms,
some of which require a list of committees as
their input, others produce a committee without
requiring input.

Now take any list of committees and feed it
as input to all those committees requiring
it - mine included.

Sorry, that's not possible. We can't use the
output as input. So we can only use any list
other than lists made from the output.

I never said that the list being fed in was the
output list. Never once did I say that an output
list was being used as input. I'd be interested
to see where you claim I said that an output list
was being used as input.

I suspect you'll ignore that challenge.

Consider the list of committees that you get
as output.

There is a committee on that list that wasn't
on the original input list, namely, the
committee my algorithm produced.

I suppose that might be. Assuming valid input.

Good.

OK. So you have agreed that whenever my algorithm
is fed with a list of committees, my algorithm will
produce a committee not on the input list.

I've said nothing about feeding output in as input,
I've said nothing about where that input list comes
from, I've just said that when my algorithm is fed
with a list of committees, my algorithm produces a
committee that's not on that input list.

And you've agreed.

That's all I wanted to show. So I don't
understand why you're claiming something
different.

I'm not claiming anything different.

Hmm.

Therefore no such algorithm exists.
You haven't shown that.
I'm claiming no algorithm can take its
output as its input.

And why was that relevant? I certainly never
claimed that my algorithm was working on its
own output.
.

Relevant Pages

  • Re: Cantor For Dummies ...
    ... If you have a real algorithm and it outputs a committee, ... If it is an actual algorithm and uses valid input. ... So we can only use any list other than lists ...
    (sci.math)
  • Re: Cantor For Dummies ...
    ... You said that your algorithm can use ANY input. ... committee C1 that wasn't on the original list. ... it turns out that is no algorithm that lists all and ... of committees or an error-free list of committees. ...
    (sci.math)
  • Re: Educated guesses for efficiency?
    ... it is comparatively rare for a program to run too slowly because an algorithm with the wrong big-O analysis was chosen. ... of things tended to be stored in lists). ... built-in sort function. ... Programmers *will* use algorithms with high complexities. ...
    (comp.lang.c)
  • Re: coerce for arbitrary types
    ... the algorithm itself is essentially last-in first-out, ... via some sort of recursion? ... WaitStack <= new stack containing topnode ... As nested lists, there's only one number in a proper position. ...
    (comp.lang.lisp)
  • Re: Comparing lists
    ... > of your faith that Big O is the be all and end all of algorithm planning. ... complexity measures, like Big-Oh. ... If experimental data and theory *disagree*: ... the conversion of lists to sets needs the insertion of N ...
    (comp.lang.python)