Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
the infinite operator, is there any research into this?
#1
The infinite operator is simply defined as:



I know that for negative integers values of b (and zero) it returns to successorship, i.e



but we also have an interesting formula, since the euler constants and the eta constants converge to 2 and 4, and since infinite iteration of eta constant x with hyper operator x results in euler constant x we have this very odd formula:



but we also know that:



and that


if this is is the root inverse of the infinite operator.

we find that
equals 4 at both 2 and 4. This means, if we want the infinite operator to be analytic and continuous, we have at least one zero in the second derivative. But we'd probably want two so that f(x) is increasing towards infinity.


Also, I was wondering, since it's completely possible to take the superfunction of the infinite operator, how would we denote that? Since it can't be should we make it something like where k is just another unit but denotes a seperate branch of superfunctions on top of the infinite operator?

for all

This means we have a flatline for the infinite operators superfunction. Interesting.
Reply
#2
in general we consider analytic as intresting , rather than local flatlines ...

you could consider your flatline as a fixpoint and that takes away some magic ...

tommy1729
Reply
#3
(07/13/2011, 12:14 PM)tommy1729 Wrote: in general we consider analytic as intresting , rather than local flatlines ...

you could consider your flatline as a fixpoint and that takes away some magic ...

tommy1729

Oh, so you're proposing


for all

Yes, you are quite right, that is much more interesting.
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 182 03/20/2018, 12:16 AM
Last Post: tommy1729
  Old Research Paper andydude 3 711 01/24/2018, 04:12 AM
Last Post: andydude
  [MO] Is there a tetration for infinite cardinalities? (Question in MO) Gottfried 10 7,733 12/28/2014, 10:22 PM
Last Post: MphLee
  Generalized arithmetic operator hixidom 16 7,591 06/11/2014, 05:10 PM
Last Post: hixidom
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 3,258 05/06/2014, 09:47 PM
Last Post: tommy1729
  Hyper operator space JmsNxn 0 1,162 08/12/2013, 10:17 PM
Last Post: JmsNxn
  Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 4,444 07/17/2013, 09:46 AM
Last Post: Gottfried
  Operator definition discrepancy? cacolijn 2 2,323 01/07/2013, 09:13 AM
Last Post: cacolijn
  Wonderful new form of infinite series; easy solve tetration JmsNxn 1 3,301 09/06/2012, 02:01 AM
Last Post: JmsNxn
  A fundamental flaw of an operator who's super operator is addition JmsNxn 2 4,445 09/06/2011, 02:00 AM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)