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