Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Infinite tetration and superroot of infinitesimal
#19
Yes I see, thank You for answers, but:

As an infinitesimal, dx in this expression is always either only positive, or only negative . And never 0. But smaller than any real (bigger if negative) . That is the definition of infinitesimal in non-standard analysis-in hyperreal set. The theory that works in calculus without using limits, so I guess application of limits in this case is misleading , but I do not know what to apply.

dx in this case is not a limit dx->0 as real, but an extension of real set, or, rather set in which reals are just subset. It is a different type of number, so to say- infinitesimal. So is 1/dx = 1/infinitesimal= definition of infinity (also belongs to hyperreals).

http://en.wikipedia.org/wiki/Non-standard_analysis
Reply


Messages In This Thread
RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/21/2007, 10:41 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 921 03/20/2018, 12:16 AM
Last Post: tommy1729
  [MO] Is there a tetration for infinite cardinalities? (Question in MO) Gottfried 10 10,834 12/28/2014, 10:22 PM
Last Post: MphLee
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 4,699 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 6,287 07/17/2013, 09:46 AM
Last Post: Gottfried
  Wonderful new form of infinite series; easy solve tetration JmsNxn 1 4,082 09/06/2012, 02:01 AM
Last Post: JmsNxn
  the infinite operator, is there any research into this? JmsNxn 2 5,114 07/15/2011, 02:23 AM
Last Post: JmsNxn
  Infinite tetration of the imaginary unit GFR 40 50,096 06/26/2011, 08:06 AM
Last Post: bo198214
  Infinite Pentation (and x-srt-x) andydude 20 24,207 05/31/2011, 10:29 PM
Last Post: bo198214
  Infinite tetration fractal pictures bo198214 15 21,340 07/02/2010, 07:22 AM
Last Post: bo198214
  Infinite towers & solutions to Lambert W-function brangelito 1 3,510 06/16/2010, 02:50 PM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)