Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
holomorphic binary operators over naturals; generalized hyper operators
#10
I've been experimenting looking at these operators and I've become much more familiar with its structure. I can prove convergence now.

Let's suppose by contradiction that; for sufficiently large n:



However. It is clear that for some

1:

Therefore we write:



Now we know that

Therefore:



However this is a contradiction because for sufficiently large the left equation becomes much larger than the right. This is easy to deduce by the relation 1 above. Therefore to prove convergence we just need add the claim:






YES! We have convergence for all s.







An important theorem I have to prove is the following, I consider it a stern requirement of hyperoperators. For all and and




I'll mull over that for awhile.

also; hopefully:

for at least
Reply


Messages In This Thread
RE: holomorphic binary operators over naturals; generalized hyper operators - by JmsNxn - 08/03/2012, 06:43 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 141 09/09/2019, 10:38 PM
Last Post: tommy1729
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 1,560 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Where is the proof of a generalized integral for integer heights? Chenjesu 2 628 03/03/2019, 08:55 AM
Last Post: Chenjesu
  Hyper-volume by integration Xorter 0 1,219 04/08/2017, 01:52 PM
Last Post: Xorter
  Hyper operators in computability theory JmsNxn 5 3,438 02/15/2017, 10:07 PM
Last Post: MphLee
  Recursive formula generating bounded hyper-operators JmsNxn 0 1,328 01/17/2017, 05:10 AM
Last Post: JmsNxn
  Rational operators (a {t} b); a,b > e solved JmsNxn 30 35,342 09/02/2016, 02:11 AM
Last Post: tommy1729
  The bounded analytic semiHyper-operators JmsNxn 2 3,264 05/27/2016, 04:03 AM
Last Post: JmsNxn
  on constructing hyper operations for bases > eta JmsNxn 1 2,439 04/08/2015, 09:18 PM
Last Post: marraco
  Bounded Analytic Hyper operators JmsNxn 25 17,987 04/01/2015, 06:09 PM
Last Post: MphLee



Users browsing this thread: 1 Guest(s)