Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Infinite tetration and superroot of infinitesimal
#21
jaydfox Wrote:If you want to treat the infinitesimal as always positive, then it's simply the logical end of the sequence dx, dx^2, dx^3, ..., dx^(1/dx). In ordinal notation, it's 1/(omega^omega), and omega^omega is a rather small ordinal in the hierarchy of countable infinities. (Not that I particularly like the hierarchy.)


(1/dx) is bigger than any n. It lies outside sequence of infinite natural numbers. (please look into non-standard analysis). It is a qualitatively different number. And after 1/dx, we still have infinite INTEGERS. What are they?
Reply


Messages In This Thread
RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/24/2007, 09:56 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 925 03/20/2018, 12:16 AM
Last Post: tommy1729
  [MO] Is there a tetration for infinite cardinalities? (Question in MO) Gottfried 10 10,851 12/28/2014, 10:22 PM
Last Post: MphLee
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 4,702 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 6,292 07/17/2013, 09:46 AM
Last Post: Gottfried
  Wonderful new form of infinite series; easy solve tetration JmsNxn 1 4,085 09/06/2012, 02:01 AM
Last Post: JmsNxn
  the infinite operator, is there any research into this? JmsNxn 2 5,118 07/15/2011, 02:23 AM
Last Post: JmsNxn
  Infinite tetration of the imaginary unit GFR 40 50,153 06/26/2011, 08:06 AM
Last Post: bo198214
  Infinite Pentation (and x-srt-x) andydude 20 24,236 05/31/2011, 10:29 PM
Last Post: bo198214
  Infinite tetration fractal pictures bo198214 15 21,375 07/02/2010, 07:22 AM
Last Post: bo198214
  Infinite towers & solutions to Lambert W-function brangelito 1 3,513 06/16/2010, 02:50 PM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)