Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Infinite tetration and superroot of infinitesimal
I have stumbled upon Time calculus while searching for substructures of infinitesimals and how to include time in mathematics.

I thought it might give a handle on infinitesimals, since, how I understand, it, structureless linear infinitesimal h->0 in derivative definition is replaced in general case by graininess to obtain normal continuous derivative.

That means that infinite tetration etc of infinitesimal can be written(?):

lim :

And superroot :lim :

And self root: lim :

The limit may depend on how depends on t since it is not obvious what will happen faster- tetration or changes in .

Gut feeling is, these speeds may be comparable.

The next question is, what will happen with this tetration and time calculus if itself is hyperoperation?

for example, ? or ? Or ?

And generally, hyperoperations in time scales might be interesting.

Please point out obvious mistakes. Thank You in advance,


Messages In This Thread
RE: Infinite tetration and superroot of infinitesimal - by Ivars - 05/10/2008, 08:33 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 1,432 03/20/2018, 12:16 AM
Last Post: tommy1729
  [MO] Is there a tetration for infinite cardinalities? (Question in MO) Gottfried 10 13,243 12/28/2014, 10:22 PM
Last Post: MphLee
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 5,642 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 7,546 07/17/2013, 09:46 AM
Last Post: Gottfried
  Wonderful new form of infinite series; easy solve tetration JmsNxn 1 4,674 09/06/2012, 02:01 AM
Last Post: JmsNxn
  the infinite operator, is there any research into this? JmsNxn 2 5,860 07/15/2011, 02:23 AM
Last Post: JmsNxn
  Infinite tetration of the imaginary unit GFR 40 59,678 06/26/2011, 08:06 AM
Last Post: bo198214
  Infinite Pentation (and x-srt-x) andydude 20 28,244 05/31/2011, 10:29 PM
Last Post: bo198214
  Infinite tetration fractal pictures bo198214 15 24,787 07/02/2010, 07:22 AM
Last Post: bo198214
  Infinite towers & solutions to Lambert W-function brangelito 1 4,105 06/16/2010, 02:50 PM
Last Post: bo198214

Users browsing this thread: 1 Guest(s)