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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Newsgroups | sci.math |
| Subject | Re: Ordinals |
| Date | 2024-02-22 19:40 +0100 |
| Message-ID | <ur84er$fkq9$1@solani.org> (permalink) |
| References | (7 earlier) <-DGdncLb25xXokv4nZ2dnZfqn_qdnZ2d@giganews.com> <ur6v5g$etpf$1@solani.org> <Jc-cnYllsrQ0Ekr4nZ2dnZfqn_GdnZ2d@giganews.com> <ur8390$fji7$5@solani.org> <ur83dl$fji7$6@solani.org> |
What we can say is the following:
i) Every set is a class
ii) Not every class is a set
So there is a hypernym / hyponym relationship
between the two. Here is are proof of i) and ii):
Proof i): Let s be a set. Then we can form
the class { x | x e s }. So there is an injection
from the sets to the classes.
Proof ii): Let V be the class { x | true },
this is the universal class which is provably
not a set. So there is no surjection from
the sets to the classes.
Hope this helps. Injection is usually taken
as indicative that two sets are in the
less than or equal relation ship, i.e. ⊆.
And lack of surjection indicates that there
is no bijection, i.e. ≠, so we have:
Sets ⊆ Classes and Sets ≠ Classes
Or together:
Sets ⊂ Classes
The difference Class \ Sets, those things
that are classes but not sets, are called
proper classes.
Mild Shock schrieb:
> I guess we have reached your intellectual
> boundaries, inherent in your squirell brain
> sized, that of a walnut, cerebrum and cerebrellum.
>
> Mild Shock schrieb:
>> Doesn't make any sense at all.
>>
>> Not a single mention of proper classes here:
>> https://plato.stanford.edu/ENTRIES/mereology/
>>
>> Ross Finlayson schrieb:
>>> Actually, for class/set distinction,
>>> I just introduced set/part distinction,
>>> and part/particle distinction,
>>> and set/particle distinction.
>>>
>>> set:class::part:particle
>>>
>>> set:part::class:particle
>>>
>>> This is a usual form that A:B::C:D is
>>> that A relates to B as C relates to D,
>>> "set is to class as part is to particle", and
>>> "set is to part as class is to particle".
>>>
>>>
>>
>
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Re: Ordinals "markus...@gmail.com" <markusklyver@gmail.com> - 2024-02-20 11:35 -0800
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-20 20:54 +0100
Re: Ordinals "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2024-02-20 11:59 -0800
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-20 12:15 -0800
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-20 12:27 -0800
Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-20 17:02 -0500
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-20 19:36 -0800
Re: Ordinals Mild Shock <bursejan@gmail.com> - 2024-02-21 05:47 -0800
Re: Ordinals Mild Shock <bursejan@gmail.com> - 2024-02-21 05:50 -0800
Re: Ordinals Mild Shock <bursejan@gmail.com> - 2024-02-21 06:16 -0800
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-21 10:24 -0800
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 09:03 +0100
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 09:11 +0100
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-22 10:16 -0800
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 19:20 +0100
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 19:22 +0100
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 19:40 +0100
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:00 +0100
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-22 10:55 -0800
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:08 +0100
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:13 +0100
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-22 11:01 -0800
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:11 +0100
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:13 +0100
Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-22 14:34 -0500
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-22 11:39 -0800
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-23 00:41 +0100
Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-21 08:33 +0000
Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-21 12:59 -0500
Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-22 13:00 +0000
Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-22 11:13 -0500
Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-23 08:47 +0000
Semanticists candy (Was: Ordinals) Mild Shock <janburse@fastmail.fm> - 2024-02-26 12:58 +0100
Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-27 14:25 -0500
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-27 11:59 -0800
Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-27 20:05 +0000
Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-27 17:24 -0500
Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-28 09:48 +0000
Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-28 06:52 -0500
Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-28 17:24 +0000
Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-02-28 17:07 -0500
Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-29 08:23 +0000
Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-02-29 07:35 -0500
Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-29 19:25 +0000
Re: Ordinals "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-29 13:48 -0800
Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-02-29 22:12 -0500
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-29 19:36 -0800
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 20:38 +0100
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 20:52 +0100
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 21:08 +0100
Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-03-01 15:56 -0500
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 22:53 +0100
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 23:11 +0100
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 23:33 +0100
Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-03-01 19:41 -0500
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-01 20:15 -0800
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-02 10:49 -0800
Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-02 20:40 +0100
Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-01 14:45 -0800
Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-03-01 08:47 +0000
Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-03-01 09:44 -0500
Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-03-01 18:29 +0000
Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-03-01 14:00 -0500
Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-03-02 12:36 +0000
Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-03-02 09:22 -0500
Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-03-02 15:25 +0000
Re: Ordinals "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2024-02-20 17:21 -0800
RSemanticists candy (Re: Ordinals) [Addendum] Mild Shock <janburse@fastmail.fm> - 2024-02-26 13:01 +0100
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