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

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

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