Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Generalized recursive operators
#1
If the operators +, *, ^, ^^, can be considered consecutive values of a sequence (with + as 1, I guess), is it possible to construct a generalized recursive function where R(1) is +, R(2) is *, and so on? In this case, can you find R(x) where x is fractional or real? I.e., is there an operator in between + and *?

[I am assuming that R(x) can be defined for positive integer x as follows: (where a and b are integers)
1. a R(x+1) (b+1) = a R(x) (a R(x+1) b)
2. a R(x+1) 1 = a
]

Additionally, has anyone considered investigating the properties as x->inf of R(x)? I would imagine that 2 R(inf) 2 is still 4 as well as x R(inf) 1 = x.
Reply


Messages In This Thread
Generalized recursive operators - by Whiteknox - 11/23/2007, 06:42 AM
RE: Generalized recursive operators - by bo198214 - 11/23/2007, 08:41 AM
RE: Generalized recursive operators - by andydude - 11/25/2007, 01:02 AM
RE: Generalized recursive operators - by andydude - 11/29/2007, 04:45 AM
RE: Generalized recursive operators - by andydude - 11/29/2007, 05:55 AM
RE: Generalized recursive operators - by andydude - 11/29/2007, 06:20 AM
RE: Generalized recursive operators - by andydude - 11/30/2007, 06:12 PM
RE: Generalized recursive operators - by andydude - 11/30/2007, 09:18 PM
RE: Generalized recursive operators - by bo198214 - 03/07/2008, 06:58 PM
RE: Generalized recursive operators - by Ivars - 02/02/2008, 10:11 PM
RE: Generalized recursive operators - by Ivars - 02/03/2008, 10:41 AM
RE: Generalized recursive operators - by andydude - 02/11/2008, 09:47 PM
RE: Generalized recursive operators - by Ivars - 02/14/2008, 06:05 PM
RE: Generalized recursive operators - by GFR - 02/03/2008, 04:12 PM
RE: Generalized recursive operators - by Ivars - 02/03/2008, 08:48 PM
RE: Generalized recursive operators - by GFR - 02/06/2008, 02:44 PM
RE: Generalized recursive operators - by Ivars - 02/06/2008, 02:56 PM
RE: Generalized recursive operators - by Ivars - 02/06/2008, 03:43 PM
RE: Generalized recursive operators - by GFR - 03/10/2008, 09:53 PM
RE: Generalized recursive operators - by GFR - 03/11/2008, 10:24 AM
RE: Generalized recursive operators - by bo198214 - 03/11/2008, 10:53 AM
RE: Generalized recursive operators - by GFR - 03/12/2008, 12:13 AM
RE: Generalized recursive operators - by GFR - 03/13/2008, 06:41 PM
RE: Generalized recursive operators - by Stan - 04/04/2011, 11:52 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Where is the proof of a generalized integral for integer heights? Chenjesu 2 696 03/03/2019, 08:55 AM
Last Post: Chenjesu
  Hyper operators in computability theory JmsNxn 5 3,566 02/15/2017, 10:07 PM
Last Post: MphLee
  Recursive formula generating bounded hyper-operators JmsNxn 0 1,372 01/17/2017, 05:10 AM
Last Post: JmsNxn
  Rational operators (a {t} b); a,b > e solved JmsNxn 30 35,979 09/02/2016, 02:11 AM
Last Post: tommy1729
  holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 15,484 08/22/2016, 12:19 AM
Last Post: JmsNxn
  The bounded analytic semiHyper-operators JmsNxn 2 3,334 05/27/2016, 04:03 AM
Last Post: JmsNxn
  Bounded Analytic Hyper operators JmsNxn 25 18,347 04/01/2015, 06:09 PM
Last Post: MphLee
  Generalized arithmetic operator hixidom 16 12,450 06/11/2014, 05:10 PM
Last Post: hixidom
  Incredible reduction for Hyper operators JmsNxn 0 2,149 02/13/2014, 06:20 PM
Last Post: JmsNxn
  Generalized Bieberbach conjectures ? tommy1729 0 1,609 08/12/2013, 08:11 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)