Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Infinite tetration and superroot of infinitesimal
#25
andydude Wrote:Before proceeding further, I would like to be precise about what an "infinitesimal" number is.
  • There exists no z such that for all real
  • There exists dz such that for all real
An infinitesimal is a number that satisfies the second property, is this correct?
How does this not form a contradiction with the first property?

Andrew Robbins

Infinitesimal is NOT a Real number at the scale we are looking at things. At the scale where Reals are Reals, Infinitesimals are not Real. Their Real part is 0, but there is more in them. Infinitesimal is definitely closer to zero, as well as closer (surrounding) to any Real than any other Real. It may be that application of relations < ; > is misleading here.

Considering Infinitesimal to be somehow Real just smaller than any Real , or have any Real part ( if it is multidimensional) in the scale we are in leads to contradiction You pointed out.
Reply


Messages In This Thread
RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/25/2007, 09:37 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 923 03/20/2018, 12:16 AM
Last Post: tommy1729
  [MO] Is there a tetration for infinite cardinalities? (Question in MO) Gottfried 10 10,849 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 5,116 07/15/2011, 02:23 AM
Last Post: JmsNxn
  Infinite tetration of the imaginary unit GFR 40 50,137 06/26/2011, 08:06 AM
Last Post: bo198214
  Infinite Pentation (and x-srt-x) andydude 20 24,233 05/31/2011, 10:29 PM
Last Post: bo198214
  Infinite tetration fractal pictures bo198214 15 21,365 07/02/2010, 07:22 AM
Last Post: bo198214
  Infinite towers & solutions to Lambert W-function brangelito 1 3,512 06/16/2010, 02:50 PM
Last Post: bo198214



Users browsing this thread: 2 Guest(s)