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Tetration of 2 and Aleph_0
#7
(09/07/2011, 08:47 PM)sheldonison Wrote: I'm no expert on set theory, but on a humorous note (not mathematically sound), assuming the generalized continuum hypothesis, then what happens if we take the slog of an aleph number?
which implies

And for any integer n where , then

Perhaps
- Shel
It turns out aleph and beth numbers should be indexed by ordinal numbers. The ordinal number equivalent to and the ordinal number equivalent to But I have no idea whether slog or sexp have any meaning for numbers. The other possibility would be to see if sexp/slog would be more applicable to ordinal numbers. But the exponentiation rules for ordinal arithmetic say that I'm unsure of what would be; the result might just be .
http://en.wikipedia.org/wiki/Ordinal_arithmetic
http://en.wikipedia.org/wiki/Aleph_number

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Messages In This Thread
Tetration of 2 and Aleph_0 - by jht9663 - 09/06/2011, 03:47 PM
RE: Tetration of 2 and Aleph_0 - by JmsNxn - 09/06/2011, 09:28 PM
RE: Tetration of 2 and Aleph_0 - by tommy1729 - 09/07/2011, 03:37 AM
RE: Tetration of 2 and Aleph_0 - by jht9663 - 09/07/2011, 03:33 PM
RE: Tetration of 2 and Aleph_0 - by sheldonison - 09/07/2011, 08:47 PM
RE: Tetration of 2 and Aleph_0 - by sheldonison - 09/09/2011, 05:54 PM
RE: Tetration of 2 and Aleph_0 - by jht9663 - 09/07/2011, 03:34 PM
RE: Tetration of 2 and Aleph_0 - by tommy1729 - 09/10/2011, 12:22 PM
RE: Tetration of 2 and Aleph_0 - by tommy1729 - 11/13/2011, 12:09 PM



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