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Posted by John Nichols on December 04, 2005 at 16:45:05 from 70.191.148.241 user Mcneacail.

such as the set of all sets which are not members of themselves

If a set is defined as the list of all sets. Then it is a member of itself as it is a set. But let us define a set of all sets but it does not include itself. But it must include itself as it is the list of all sets. So we have a problem. The set of all sets can not be an empty set, which may also be part of the problem. The empty set contains no elements. An example, the set of all positive integers less then zero is an empty set.

The problem may be related to the simple definition of a set.

In a way this is a way to start recursion. A process that calls itself. Let us say you have a list of {a,b,c,d,e} and you recursively move down the list. Call(One) returns a. Call(Two) returns b. down to call(5) returns e. The problem is Call(6) returns nothing, but it would be nice if it returned the list and you could start again.

It is at this point, whilst brushing my teeth this morning that I realized a direct relationship to AR and SA's for this stuff. One member of the group of the SAD's use this type of logic, call it recursion, albeit in a simple fashion in the books. Rather than spoil a good thread early I am going to leave it for a day and see if anyone spots the idea as well.

(Just so no one thinks I am stealing any ideas I will email Jock with my thought.) Actually it will be interesting to see if there are any others in the books.

JMN



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