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Groups > comp.lang.javascript > #29540
| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Newsgroups | comp.lang.javascript |
| Subject | Re: passing a set of numbers to a function |
| Date | 2016-02-05 14:13 +0000 |
| Organization | A noiseless patient Spider |
| Message-ID | <87zivfkzyi.fsf@bsb.me.uk> (permalink) |
| References | (3 earlier) <dna6bbll0vvjn3gvovc9t822fduak5inlu@4ax.com> <87r3gso59h.fsf@bsb.me.uk> <1603158.xI32ru06Pi@PointedEars.de> <58b65993-5943-4f8e-a4e2-9e97bb1feea3@googlegroups.com> <n926p5$rqt$1@news.albasani.net> |
Stefan Weiss <krewecherl@gmail.com> writes:
> On 02/05/2016 01:19, Scott Sauyet wrote:
>> There is a simple way to implement mathematical sets, finite or
>> infinite using predicate functions. [...]
>>
>> But for those interested in sets which have the normal set operations
>> of `contains`, `union`, `intersection`, and `complement`, the
>> following looks to be quite simple:
>>
>> const set = pred => ({
>> contains: pred,
>> union: set2 => set(val => pred(val) || set2.contains(val)),
>> intersection: set2 => set(val => pred(val) && set2.contains(val)),
>> complement: () => set(val => !pred(val))
>> });
>>
>> One could use this to create sets such as these:
>>
>> const fizz = set(n => n % 3 == 0);
>> const buzz = set(n => n % 5 == 0);
>> const fizzBuzz = fizz.intersection(buzz);
>> const fizzOrBuzz = fizz.union(buzz);
>> const notBuzz = buzz.complement();
>
> A very nice example.
>
> [snip tests]
>
>> But, for one trying to use a set as a Collection, these are missing
>> several important features. Obviously there is no way to add or
>> remove members. There is also no generic way to iterate, although
>> obviously one could create iterators to match specific Sets. So,
>> while this is reasonably close to mathematical sets, they are not
>> really close to what are usually considered sets in software.
>>
>> 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?
If S1 \subset S2 and S2 \subset S1 then S1 = S2. Hence a correct subset
predicate could determines if two functions compute the same value in
all cases.
Similarly, you can't implement an isEmpty predicate either and, as Scott
suggested, I think some version of Rice's theorem will come into play so
that no "interesting" property of sets of sets will be decidable.
(I'm not knocking the method. This is what I had in mind when I talked
about implementing infinite sets because membership was, at that point,
the only operation that was wanted.)
> "intersection" already does that. The same would go
> for adding or removing individual members or (sub)sets, using "union"
> and "intersection", respectively.
>
> 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.
That's a hot topic! See the well-ordering theorem of ZFC. Mind you,
this is obviously not ZFC since it can express Russell's paradox:
function russell(m, s) { return s.contains(m); }
const R = set(x => !russell(x, x));
R.contains(R);
<snip>
--
Ben.
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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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