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| Subject:
Set Theory Proof - Need no later than Noon PST May 13, 2005 ... or not at all.
Category: Miscellaneous Asked by: thecuriousone-ga List Price: $2.00 |
Posted:
12 May 2005 21:06 PDT
Expires: 13 May 2005 01:13 PDT Question ID: 521161 |
Assuming the Axiom of Choice (AC) you can show that aleph_1 is not a countable union of countable sets and, further, that you need SOME choice (namely Countable Choice (AC_w)). Show in ZF (without any choice) that aleph_2 is not a countable union of countable sets. [Note: The following hint may help: Suppose for contradiction that aleph_2 is a countable union of contable sets. Let alpha_n be the ordertype of X_n and let alpha be the countable union of alpha_n. Violate the fact that aleph_2 is a cardinal.] |
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| Subject:
Re: Set Theory Proof - Need no later than Noon PST May 13, 2005 ... or not at all.
From: politicalguru-ga on 13 May 2005 00:07 PDT |
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