Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Infinite tetration and superroot of infinitesimal
#10
First, if I were you, I would not use i for this infinitesimal construction, as it is not related to the imaginary unit at all. I would use z instead, to be clear, and since the numbers are close to zero. Second, it sounds like your definition of infinitesimals are equivalent to the reciprocals of ordinal numbers, since you talk about (mirroring ) and "infinities of the same order", so you might be better off, and able to communicate your ideas better if you simply define your transfinitesimals in terms of Cantor's ordinal numbers instead. So you could define your infinitesimals as: in terms of the first transfinite ordinal number .

My only problem with this is that I have a deep-seated hatred of Cantor's numbers. I'll save that talk for later.

Andrew Robbins
Reply


Messages In This Thread
RE: Infinite tetration and superroot of infinitesimal - by andydude - 12/20/2007, 06:31 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 1,169 03/20/2018, 12:16 AM
Last Post: tommy1729
  [MO] Is there a tetration for infinite cardinalities? (Question in MO) Gottfried 10 12,074 12/28/2014, 10:22 PM
Last Post: MphLee
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 5,195 05/06/2014, 09:47 PM
Last Post: tommy1729
  Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 6,937 07/17/2013, 09:46 AM
Last Post: Gottfried
  Wonderful new form of infinite series; easy solve tetration JmsNxn 1 4,389 09/06/2012, 02:01 AM
Last Post: JmsNxn
  the infinite operator, is there any research into this? JmsNxn 2 5,499 07/15/2011, 02:23 AM
Last Post: JmsNxn
  Infinite tetration of the imaginary unit GFR 40 55,174 06/26/2011, 08:06 AM
Last Post: bo198214
  Infinite Pentation (and x-srt-x) andydude 20 26,254 05/31/2011, 10:29 PM
Last Post: bo198214
  Infinite tetration fractal pictures bo198214 15 23,166 07/02/2010, 07:22 AM
Last Post: bo198214
  Infinite towers & solutions to Lambert W-function brangelito 1 3,818 06/16/2010, 02:50 PM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)