09/09/2011, 05:54 PM
(This post was last modified: 09/09/2011, 08:23 PM by sheldonison.)

(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?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 .

which implies

And for any integer n where , then

Perhaps

- Shel

http://en.wikipedia.org/wiki/Ordinal_arithmetic

http://en.wikipedia.org/wiki/Aleph_number