07/30/2009, 06:31 AM

(02/14/2008, 10:41 PM)GFR Wrote:Ivars Wrote:Have You considered "+" zeration and "-" zeration?

Not really. But there is some work carried on for "mapping" the numbers obtained by its inverse operation. They ... risk ... to be multivalued objects, similar, in some cases, to the logarithms of negative real numbers. There might perhaps also exist hyperoperations with negative ranks, giving, for instance:

a@a = ao2

aoa = a+2

a+a = a*2

......

But, this requires a ... more active intervention of KAR in this discussion.

GFR

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That "@" operation or the s=-1 operation, I find interesting. I did my own research and realized the operations below zero must not be functions when you use the operation that's not the opposite.

I discovered that

2@4= 4 and 5

3@5= 5 and 6

6@7= 7 and 8

6@8= 8 and 9

This only works if you accept Kar's zeration.

below s=0, they are all +1 operation, but they are +1 for a longer range of numbers before its +2, ie 6@6@6 is 6 zeration 3 which is 7 until 6@6@6@6@6@6 which is 8.

let me know what you think.