(10/01/2014, 08:40 AM)tommy1729 Wrote: ........
To understand tetration you need to understand +,*,^ at least.
To understand ^ you need to understand *.
To understand * you need to understand +.
Defining and understanding a hyperoperator seems to require the lower hyperoperators.
But with zeration that is A PROBLEM.
.....
..... properties like distributive require use of a lower hyperoperator : a * (b+c) = a*b + a*c.
....
Zeration seems to lack properties and therefore consistancy.
regards
tommy1729
As a matter of fact, if you apply these principles, you would indeed discover a problem with ... 'Addition', because:
"To understand + you (would) need to understand o!". In fact, we should have (sorry for 'o' and, please, forget 'some' useless brackets):
a * a = a ^ 2; a * (a * a) = a ^ 3
a + a = a * 2; a + (a + a) = a * 3
a o a = a + 2; a o (a o a) = a + 3.
And, moreover, as we have seen:
a + (b o c) = (a + b) o (a + c), i.e. the 'descending' distributivity seems to hold! And ... to gain consistency!
And, don't forget: 2o2 = 2+2 = 2*2 = 2^2 = 2#2 = .... 2[s]2 = 4. The 'Magic Four' relation!
Thank you for your interest. Best regards.
GFR