Thread Rating:
  • 1 Vote(s) - 4 Average
  • 1
  • 2
  • 3
  • 4
  • 5
the distributive property
#5
As you know these are a generalization of the Bennet Hyperoperations (Commutative Hyperoperations).

I usually use this notation for them because i find it very confortable




Bennet Hyperoperations are a special case of these (with the natural base )


and is the max operation while is the min operation(this limit process is related with the litinov-maslov dequantization of the semifield of non-negative real numbers in to the Tropical semifield )
------------------------

I apologize in advance if I did not understand your conjecture but i think that is not true at all.

In general we have that the operations are different when base changes

only if

If you quickly plot the graps of for differents bases you see that the the result changes.

Notice that the identity element of is
--------------------------

About tetration: yes! There is an interesting link because an extension of tetration will bring to us the fractional rank operations of this Hyperoperation family (JmsNxn already worked on something similar in his thread on logarithmic semi-operators http://math.eretrandre.org/tetrationforu...+operators)


MathStackExchange account:MphLee

Fundamental Law
Reply


Messages In This Thread
the distributive property - by tommy1729 - 09/25/2010, 12:05 AM
RE: the distributive property - by tommy1729 - 09/28/2010, 12:22 PM
RE: the distributive property - by tommy1729 - 10/13/2010, 11:07 PM
RE: the distributive property - by tommy1729 - 05/23/2014, 11:12 PM
RE: the distributive property - by MphLee - 05/24/2014, 09:46 AM
RE: the distributive property - by tommy1729 - 05/25/2014, 12:16 AM
RE: the distributive property - by MphLee - 05/25/2014, 09:35 AM
RE: the distributive property - by tommy1729 - 05/26/2014, 11:37 PM
RE: the distributive property - by MphLee - 05/27/2014, 07:43 AM
RE: the distributive property - by tommy1729 - 05/27/2014, 12:23 PM
RE: the distributive property - by MphLee - 05/27/2014, 12:46 PM
RE: the distributive property - by tommy1729 - 05/27/2014, 10:49 PM
RE: the distributive property - by andydude - 05/27/2014, 07:45 PM
RE: the distributive property - by MphLee - 05/27/2014, 08:22 PM
RE: the distributive property - by tommy1729 - 05/27/2014, 10:55 PM
RE: the distributive property - by MphLee - 06/06/2014, 09:56 AM
RE: the distributive property - by tommy1729 - 06/06/2014, 11:56 AM
RE: the distributive property - by MphLee - 06/06/2014, 12:09 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  How many methods have this property ? tommy1729 1 4,559 05/22/2014, 04:56 PM
Last Post: sheldonison
  Distributive "tetration", is this possible JmsNxn 6 11,280 09/05/2011, 11:58 PM
Last Post: tommy1729
  Iterations of ln(mod(ln(x^(1/x))) and number with property Left a[4]n=exp (-(a^(n+1)) Ivars 0 4,023 03/30/2008, 06:41 PM
Last Post: Ivars



Users browsing this thread: 1 Guest(s)