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Zeration = inconsistant ?
#6
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
Reply


Messages In This Thread
Zeration = inconsistant ? - by tommy1729 - 10/01/2014, 08:40 AM
RE: Zeration = inconsistant ? - by MphLee - 10/01/2014, 11:27 AM
RE: Zeration = inconsistant ? - by GFR - 10/02/2014, 02:44 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 09:27 PM
RE: Zeration = inconsistant ? - by MphLee - 10/02/2014, 10:02 PM
RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 09:58 AM
RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 10:58 PM
RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:29 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:11 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 11:11 PM
RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:39 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:12 PM
RE: Zeration = inconsistant ? - by MphLee - 10/03/2014, 09:20 AM
RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:32 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:41 PM
RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 10:19 AM
RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 11:24 AM
RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:16 PM
RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 12:58 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 10:20 PM
RE: Zeration = inconsistant ? - by MphLee - 10/05/2014, 03:36 PM

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