Re: Cantor For Dummies ...

On Mar 29, 4:18 am, riderofgiraffes <mathforum.org...@xxxxxxxxxxxxxx>
wrote:


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.

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

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

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

That's not relevent.

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 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.

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

Sounds good to me.

...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. 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.

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.

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 its in the list
of algorithms that generate committees.

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

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.

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.

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

I'm not claiming anything different.

Therefore no such algorithm exists.

You haven't shown that.

I'm claiming no algorithm can take its output as
its input.

.

Relevant Pages

  • Re: Cantor For Dummies ...
    ... algorithms that output a committee can be listed. ... committee output by my algorithm depends on its input. ... If it is an actual algorithm and uses valid input. ... other than lists made from the output. ...
    (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: 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)
  • 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)