Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Continuum sums -- a big problem and some interesting observations
The same is true for integrals: if you take

you can get different functions wich differ not only by a constant. The convention here is to count the solution as but this is only one of possible solutions. Another for example is

You can also claim that there are two solutions ln x and ln (-x) which suitable only for one half of the domain of definition. In fact neither of them is the solution for the function on the whole real axis.

By analogy with logarithm it is reasonable to count that



This is a graph of how it looks like:
[Image: h_1286684374_10064fb295.png]

Just use absolute values and you'll get a compact form for the solution. For integrals the conventional form is determined by the Cauchy principal value.

Messages In This Thread
RE: Continuum sums -- a big problem and some interesting observations - by Ansus - 10/09/2010, 03:13 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Interesting commutative hyperoperators ? tommy1729 0 95 02/17/2020, 11:07 PM
Last Post: tommy1729
  Very interesting topic Ansus 0 466 10/01/2019, 08:14 PM
Last Post: Ansus
  THE problem with dynamics tommy1729 1 2,493 04/04/2017, 10:52 PM
Last Post: tommy1729
  [sci.math] halting problem skeptic. tommy1729 0 1,787 05/30/2015, 09:24 PM
Last Post: tommy1729
  2015 Continuum sum conjecture tommy1729 3 3,565 05/26/2015, 12:24 PM
Last Post: tommy1729
  Problem with cauchy method ? tommy1729 0 1,977 02/16/2015, 01:51 AM
Last Post: tommy1729
  Another way to continuum sum! JmsNxn 6 6,807 06/06/2014, 05:09 PM
Last Post: MphLee
  Further observations on fractional calc solution to tetration JmsNxn 13 14,562 06/05/2014, 08:54 PM
Last Post: tommy1729
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 5,419 05/06/2014, 09:47 PM
Last Post: tommy1729
  On naturally occuring sums tommy1729 0 2,028 10/24/2013, 12:27 PM
Last Post: tommy1729

Users browsing this thread: 1 Guest(s)