10/02/2014, 10:58 PM
It feels a bit strange ...
A so called new concept " zeration " being almost equivalent to max[a,b].
Max[a,b] does not seem so intresting as a function.
Max[12,100] = Max[13,100] = Max[91,100]
Nothing special.
zeration also still seems undefined or inconsistant for complex arguments.
(15 + 13 i) [0] (- 41 +91 i) = ??
Consider Trapmann's solution :
Max(a+2,b+1)
This fails to be commutative !
Also Max does not have AN INTRESTING DERIVATIVE.
Also iterations of max are usually not intresting.
So , no complex numbers , no intresting calculus , no intresting dynamics.
Also there is not much algebra or geometry about Max.
Max+ algebra being a big exception.
It seems tetration is more intresting than zeration.
Zeration seems to loose properties rather then to gain ?
A possible solution to that is finding intresting properties afterall for max or finding another zeration.
Or ...
Finding addional must-have properties.
1) commutative and distributive
solution : max(a,b) + kroneckerdelta(a,b) + 1
Notice this is not (even) differentiable near a = b.
Can we do better ?
Im sure there are many nice algorithms that use max.
( even without max+ algebra )
Maybe one of those could help us out.
---
Assume we agree on
zeration(a,b)
= max(a,b) + kroneckerdelta(a,b) + 1.
What would then be the next question ??
" -1-ation " ?
abel functions / superfunctions of zeration ?
numerical methods based on zeration ?
( not equal to those from max+ algebra ofcourse ... remember we want to talk about NEW things right ? )
regards
tommy1729
A so called new concept " zeration " being almost equivalent to max[a,b].
Max[a,b] does not seem so intresting as a function.
Max[12,100] = Max[13,100] = Max[91,100]
Nothing special.
zeration also still seems undefined or inconsistant for complex arguments.
(15 + 13 i) [0] (- 41 +91 i) = ??
Consider Trapmann's solution :
Max(a+2,b+1)
This fails to be commutative !
Also Max does not have AN INTRESTING DERIVATIVE.
Also iterations of max are usually not intresting.
So , no complex numbers , no intresting calculus , no intresting dynamics.
Also there is not much algebra or geometry about Max.
Max+ algebra being a big exception.
It seems tetration is more intresting than zeration.
Zeration seems to loose properties rather then to gain ?
A possible solution to that is finding intresting properties afterall for max or finding another zeration.
Or ...
Finding addional must-have properties.
1) commutative and distributive
solution : max(a,b) + kroneckerdelta(a,b) + 1
Notice this is not (even) differentiable near a = b.
Can we do better ?
Im sure there are many nice algorithms that use max.
( even without max+ algebra )
Maybe one of those could help us out.
---
Assume we agree on
zeration(a,b)
= max(a,b) + kroneckerdelta(a,b) + 1.
What would then be the next question ??
" -1-ation " ?
abel functions / superfunctions of zeration ?
numerical methods based on zeration ?
( not equal to those from max+ algebra ofcourse ... remember we want to talk about NEW things right ? )
regards
tommy1729