Re: math : inaccessible cardinal
- From: Tim Little <tim@xxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Mon, 31 Mar 2008 00:41:17 -0000
On 2008-03-30, amy666 <tommy1729@xxxxxxxxxxx> wrote:
to go from aleph_x to aleph_(x+1) we do the operation
"2^".
You might, but we don't. To go from aleph_x to aleph_(x+1) we take
the least ordinal of greater cardinality than aleph_x. The powerset
axiom is useful for showing that such a thing exists, but the powerset
operation isn't part of the definition itself.
what do we need to do to get from aleph_aleph_0 to
aleph_aleph_1. ???
Aleph_alpha is defined for all ordinals alpha. See e.g.
http://en.wikipedia.org/wiki/Aleph_number#Aleph-.CE.B1_for_general_.CE.B1
Both aleph_0 and aleph_1 are infinite limit ordinals, so substitute
into the appropriate definition.
amy
well ?
"well" what? Once again you're "quoting" an article that doesn't seem
to be on my news servers, and isn't referenced in the headers of your
post. If you ever made such a post, it could have been on some
private site for all I can tell. If you want a reply here on Usenet,
post the original message here on Usenet.
- Tim
.
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