01/31/2008, 06:20 PM
Hi, Henryk!
You mentioned the following "Idea stub 2", concerning a possible extension of the reals to infinite ... entities and, particularly, the use of tetration for clearly representing the "limit epsilon-1" infinite Cantor's ordinal, as follows:
I agree that, in general, hyperoperations could be an excellent tool for further "extending epsilon1" , via pentation hexation etc, up to "omegation". We (KAR & GFR) already presented this idea to the NKS Forum (see: Hyperoperations, second progress report). A new "limit" would then appear: w[w]w = omega-omega-omega which could probably be taken for (Capital) OMEGA, the (first?) uncountable infinite ordinal. Good grief.
GFR
You mentioned the following "Idea stub 2", concerning a possible extension of the reals to infinite ... entities and, particularly, the use of tetration for clearly representing the "limit epsilon-1" infinite Cantor's ordinal, as follows:
bo198214 Wrote:And idea stub 2.
I agree that, in general, hyperoperations could be an excellent tool for further "extending epsilon1" , via pentation hexation etc, up to "omegation". We (KAR & GFR) already presented this idea to the NKS Forum (see: Hyperoperations, second progress report). A new "limit" would then appear: w[w]w = omega-omega-omega which could probably be taken for (Capital) OMEGA, the (first?) uncountable infinite ordinal. Good grief.
GFR
