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Topic: Using classes instead of sets
Replies: 26   Last Post: Apr 1, 2013 8:04 PM

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 Paul Posts: 780 Registered: 7/12/10
Re: Using classes instead of sets
Posted: Mar 28, 2013 10:43 AM

On Thursday, March 28, 2013 1:45:34 PM UTC, Frederick Williams wrote:
...
>
> Often one studies all groups, or all groups of a certain kind. Are
>
> those collections classes?

...

They are always classes and sometimes sets. A class is more general than a set so any collection which is a set is also a class. If we define isomorphic groups as being equal (as everyone does), then the collection of finite groups is a countably infinite set and we can talk about "the set of finite groups".

However, the collection of groups is "too big" to be a set. Hence that collection is a class which is not a set. "Too big" because it contains a subcollection which corresponds to the class of all ordinals.

Paul Epstein

Date Subject Author
3/27/13 Stuart M Newberger
3/28/13 Paul
3/28/13 Frederick Williams
3/28/13 Paul
3/28/13 Frederick Williams
3/28/13 Paul
3/28/13 Kaba
3/28/13 David C. Ullrich
3/28/13 Herman Rubin
3/28/13 Frederick Williams
3/28/13 Frederick Williams
3/28/13 Ken.Pledger@vuw.ac.nz
3/28/13 fom
3/28/13 Herman Rubin
3/28/13 ross.finlayson@gmail.com
3/28/13 fom
3/28/13 Herman Rubin
3/29/13 Shmuel (Seymour J.) Metz
3/30/13 fom
3/30/13 Shmuel (Seymour J.) Metz
3/30/13 David C. Ullrich
3/30/13 Shmuel (Seymour J.) Metz
3/31/13 Frederick Williams
3/30/13 Guest
4/1/13 Shmuel (Seymour J.) Metz