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Re: passing a set of numbers to a function

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On 02/05/2016 14:45, Scott Sauyet wrote:
> Stefan Weiss wrote:
>> Scott Sauyet wrote:
>>> We should also note that this misses at least one important notion 
>>> from mathematics as well.  I'm fairly certain that there is no way to 
>>> write a `subset` function.
>>
>> Why? Wouldn't "subset" just be one more predicate to be combined with
>> the set's predicate? "intersection" already does that. The same would go
>> for adding or removing individual members or (sub)sets, using "union"
>> and "intersection", respectively.
> 
> I just had the same realization about adding and removing members.

Yes, we do tend to post to this group at the same time. Odd :)

> But unless I'm missing something fundamental, I don't see how `subset`
> would work in the general case.  It's not an operation like `intersection`
> `union`, `add`, etc, but a predicate like `contains`.
> 
> If you are given `set(fn)` and want to know if set(x => x == ~~x)
> (the integers) is a subset of it, how would you test? What if fn was x =>
> x == ~~x && x != 9007199254740990?

Ah, I misunderstood what you meant by "a subset function". I took it to
mean "get a subset (fn)", not "is a subset (set)". The former is
basically the same as intersection, the latter may indeed be impossible.
This is beyond my amateur mathematical knowledge.

>> As for iterators, sets don't have an inherent order, so any kind of
>> ordered iteration would be an extension to the concept. The ability to
>> produce members, in any order, is also not a required property of a set.
> 
> Right, but most software implementations of set make it part of some
> group of types that can be iterated.  Since the storage mechanism would
> generally allow one to impose an order, even if it's not logical (think
> Java's hash-code order, for instance), it's not too strange to assume
> that a (finite) set can be iterated.  Of course this makes no sense at
> all for an uncountably infinite set.

Or even countably infinite :)

I think my point (also concerning the rest of the snipped text) is that
a purely predicate-based set implementation makes sense, and so does the
storage-based implementation. But I don't think the two can be combined.
The whole point of the predicate-based version (IMO) is to eliminate the
need for storage (= enumerating all elements). It might gain the ability
for iteration, but it would lose its descriptive nature and could no
longer handle infinite sets.


Having just read Ben's replies, I think I'll quietly back away now...
this goes way beyond my naive understanding of sets. Although I should
have remembered Russel's paradox. I recently read Logicomix, a
fascinating graphic novel about the search for the foundations of
mathematics, loosely based on Russel's life.


- stefan

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passing a set of numbers to a function Matheus Suffi <matheus.suffi40@gmail.com> - 2016-01-25 04:45 -0800
  Re: passing a set of numbers to a function Aleksandro <aleksandro@gmx.com> - 2016-01-25 10:51 -0300
  Re: passing a set of numbers to a function Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-01-29 03:57 +0100
    Re: passing a set of numbers to a function Joao Rodrigues <groups_jr-1@yahoo.com.br> - 2016-01-28 23:19 -0800
      Re: passing a set of numbers to a function Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-29 10:09 +0000
        Re: passing a set of numbers to a function John Harris <niam@jghnorth.org.uk.invalid> - 2016-01-29 10:20 +0000
          Re: passing a set of numbers to a function Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-29 12:23 +0000
            Re: passing a set of numbers to a function John Harris <niam@jghnorth.org.uk.invalid> - 2016-01-29 14:50 +0000
              Re: passing a set of numbers to a function Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-29 16:11 +0000
                Re: passing a set of numbers to a function John Harris <niam@jghnorth.org.uk.invalid> - 2016-01-30 10:10 +0000
          Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-01-29 08:35 -0800
            Re: passing a set of numbers to a function John Harris <niam@jghnorth.org.uk.invalid> - 2016-01-30 10:34 +0000
              Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-01-30 18:53 -0800
                Re: passing a set of numbers to a function John Harris <niam@jghnorth.org.uk.invalid> - 2016-01-31 14:50 +0000
                Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-01-31 09:56 -0800
                Re: passing a set of numbers to a function John Harris <niam@jghnorth.org.uk.invalid> - 2016-02-01 11:02 +0000
                Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-02-01 18:10 -0800
        Re: passing a set of numbers to a function Gene Wirchenko <genew@telus.net> - 2016-01-29 09:38 -0800
          Re: passing a set of numbers to a function Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-29 20:17 +0000
        Re: passing a set of numbers to a function Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-01-29 20:08 +0100
    Re: passing a set of numbers to a function Aleksandro <aleksandro@gmx.com> - 2016-01-29 10:32 -0300
      Re: passing a set of numbers to a function "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2016-01-29 14:53 +0100
        Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-01-29 06:26 -0800
    Re: passing a set of numbers to a function John Harris <niam@jghnorth.org.uk.invalid> - 2016-01-29 14:19 +0000
      Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-01-29 08:38 -0800
        Re: passing a set of numbers to a function Aleksandro <aleksandro@gmx.com> - 2016-01-29 13:54 -0300
          Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-01-29 10:11 -0800
            Re: passing a set of numbers to a function Aleksandro <aleksandro@gmx.com> - 2016-01-29 15:38 -0300
            Re: passing a set of numbers to a function Anders Wegge Keller <wegge@geostat.dk> - 2016-01-29 20:13 +0100
              Re: passing a set of numbers to a function Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-01-29 20:46 +0100
                Re: passing a set of numbers to a function Aleksandro <aleksandro@gmx.com> - 2016-01-29 16:59 -0300
          Re: passing a set of numbers to a function Erwin Moller <erwinmollerusenet@xs4all.nl> - 2016-02-12 12:03 +0100
  Re: passing a set of numbers to a function Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-02 11:18 +0100
    Re: passing a set of numbers to a function Aleksandro <aleksandro@gmx.com> - 2016-02-02 12:31 -0300
    Re: passing a set of numbers to a function John Harris <niam@jghnorth.org.uk.invalid> - 2016-02-04 10:42 +0000
      Re: passing a set of numbers to a function Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-02-04 15:38 +0000
        Re: passing a set of numbers to a function Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-04 17:33 +0100
          Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-02-04 16:19 -0800
            Re: passing a set of numbers to a function Stefan Weiss <krewecherl@gmail.com> - 2016-02-05 14:06 +0100
              Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-02-05 05:45 -0800
                Re: passing a set of numbers to a function Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-02-05 14:34 +0000
                Re: passing a set of numbers to a function Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-02-05 15:42 +0000
                Re: passing a set of numbers to a function Stefan Weiss <krewecherl@gmail.com> - 2016-02-05 16:04 +0100
                Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-02-05 10:48 -0800
                Re: passing a set of numbers to a function Stefan Weiss <krewecherl@gmail.com> - 2016-02-06 04:50 +0100
                Re: passing a set of numbers to a function "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2016-02-06 10:05 -0800
                Re: passing a set of numbers to a function Stefan Weiss <krewecherl@gmail.com> - 2016-02-06 23:30 +0100
                Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-02-06 17:32 -0800
              Re: passing a set of numbers to a function Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-02-05 14:13 +0000
                Re: passing a set of numbers to a function Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-02-05 17:15 +0000
            Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-02-05 05:19 -0800
              Re: passing a set of numbers to a function Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-02-05 13:43 +0000
                Re: passing a set of numbers to a function Scott Sauyet <scott.sauyet@gmail.com> - 2016-02-05 06:08 -0800
        Re: passing a set of numbers to a function Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-02-04 20:25 +0000
        Re: passing a set of numbers to a function John Harris <niam@jghnorth.org.uk.invalid> - 2016-02-05 10:51 +0000

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