Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Additional super exponential condition
I was just thinking about the following for an arbitrary super exponential :
We surely have for natural numbers m and n that

So why not demand this rule also for the super exponential extended to the reals?

For a super logarithm the rule would be:

Note that this rule is not applicable to the left-bracketed super exponentials.
Because from the rule it follows already that:
which is not valid for left bracketed super exponentials because they grow more slowly.

I didnt verify the rule yet for our known tetration extensions. Do you think it will be valid?

However I dont think that this condition suffice as a uniqueness criterion. But at least it would reduce the set of valid candidates.
bo198214 Wrote:For a super logarithm the rule would be:

This is certainly consistent. For example:

which is true.

Andrew Robbins
Ansus Wrote:By the way, I had an idea to extend hyper-operator based on the sequence of mean values:
And how? I.e. what is ?
Ansus Wrote:

Ya of course, but what is ? You said you have an idea how to extend it to real via those means.
I doubt this is an option to extend the mean value operations.
In a given set of data (say a1, a2, ...), ordering is irrelevant for calculating a mean value. But a1^a2(^ is different from a2^a1(^a3...). Well, at least most of the time.

Possibly Related Threads...
Thread Author Replies Views Last Post
  Is bugs or features for super-logarithm? Ember Edison 10 14,817 08/07/2019, 02:44 AM
Last Post: Ember Edison
  A fundamental flaw of an operator who's super operator is addition JmsNxn 4 12,134 06/23/2019, 08:19 PM
Last Post: Chenjesu
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 15,646 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Inverse super-composition Xorter 11 25,045 05/26/2018, 12:00 AM
Last Post: Xorter
  Math overflow question on fractional exponential iterations sheldonison 4 9,486 04/01/2018, 03:09 AM
Last Post: JmsNxn
  The super 0th root and a new rule of tetration? Xorter 4 8,978 11/29/2017, 11:53 AM
Last Post: Xorter
  Solving tetration using differintegrals and super-roots JmsNxn 0 3,636 08/22/2016, 10:07 PM
Last Post: JmsNxn
  Removing the branch points in the base: a uniqueness condition? fivexthethird 0 3,133 03/19/2016, 10:44 AM
Last Post: fivexthethird
  The super of exp(z)(z^2 + 1) + z. tommy1729 1 4,873 03/15/2016, 01:02 PM
Last Post: tommy1729
  Super-root 3 andydude 10 20,672 01/19/2016, 03:14 AM
Last Post: andydude

Users browsing this thread: 1 Guest(s)