March 5th, 2018, 11:08 AM  #21  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,282 Thanks: 93  Quote:
If Sn=$\displaystyle 2^{n}$, what is $\displaystyle \lim_{n \rightarrow \infty}$Sn? By definition $\displaystyle 2^{n}$ = 2x2x2x2x x2 to n places. $\displaystyle \lim_{n \rightarrow \infty}$Sn = 2x2x2x2x... for an endless string of 2's, which, by the way, is in {Sn}. Last edited by skipjack; March 5th, 2018 at 05:28 PM.  
March 5th, 2018, 11:21 AM  #22 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,214 Thanks: 2410 Math Focus: Mainly analysis and algebra  I wrote the first question again in my post. Zylo said that he didn't answer it correctly, so I've asked it again. Of course, he's decided to answer a different one that doesn't force him to confront the problem that it highlights.

March 5th, 2018, 12:03 PM  #23 
Global Moderator Joined: Dec 2006 Posts: 18,686 Thanks: 1522  
March 5th, 2018, 05:04 PM  #24  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,757 Thanks: 1008 Math Focus: Elementary mathematics and beyond  Quote:
@zylo: Please respond to the direction implied by v8archie's post. If you're not sure what that is then ask. @all other members I'm asking that all activity here be suspended until zylo has complied with my request above. Thank you. (Discussion will resume when appropriate).  
March 5th, 2018, 07:01 PM  #25  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,214 Thanks: 2410 Math Focus: Mainly analysis and algebra 
All my questions stemmed from the response to the first one, which Zylo eventually indicated that he had answered incorrectly by giving an interpretation that he says is irrelevant. That being the case, I don't really see any value in rehashing any of the questions other than the first, which I restated in the post and which I quote here. Quote:
The second element of the limiting case is 000...001, which is an infinite sequence of zeros followed by a 1 Of course, that doesn't make any sense because you can't have something that follows an infinite sequence because an infinite sequence never ends by definition.If the second element in the limiting case isn't well defined, the limiting case itself will be illdefined and thus different to Cantor's list of infinite binary sequences.  
March 9th, 2018, 08:23 AM  #26 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,282 Thanks: 93 
Responding to the direction implied by v8archie post's is impossible because they are vaque and loaded with generalities and judgements about unspecified posts. Therefore I will start a new thread with what I intended to post here. Last edited by zylo; March 9th, 2018 at 08:31 AM. 
March 9th, 2018, 08:49 AM  #27 
Senior Member Joined: Aug 2012 Posts: 1,763 Thanks: 480  
March 9th, 2018, 08:51 AM  #28 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,282 Thanks: 93  
March 9th, 2018, 09:07 AM  #29 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,282 Thanks: 93 
You made a mistake closing: Cantor's Diagonal Argument which was: "Suppose I have a set of all infinite sequences of binary digits. Either I know the digits of each sequence or I don't. If I don't, how do I know they are all different? If I do, I can arrange them in numerical (countable) order. The list has a smallest member 0, and I can decide which of any two members is larger."  The response, which I was about to make before the thread was closed, is: It is legitimate to assume the sequences are all different. In That case I can empty the set systematically and put each sequence in a list, assured that each time I get another one it is different. That's the problem with prejudicial, uninformed, censorship, which is the antithesis of mathematics. EDIT Counter counter argument: If the set exists, I can put it's members in numeric order because I can place each arbitrarily selected member in order. For example, if the list consists of "1"and "3," then I can place "2" between them. I would never have started another thread if it weren't for arbitrary demands (threats) made by greg1313. Last edited by zylo; March 9th, 2018 at 09:45 AM. 
March 9th, 2018, 09:58 AM  #30 
Global Moderator Joined: Dec 2006 Posts: 18,686 Thanks: 1522 
What do you mean by "systematically"? Wouldn't it be simpler to start with all possible distances along a line segment measured from one end of it? They would come already in order of magnitude. However, that wouldn't mean that you could "systematically" list them. The first (smallest) would be zero, but what would the second one be?


Tags 
binary, cantor, infinite, sequence 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Is an Infinite Binary Sequence a Natural Number?  zylo  Real Analysis  45  July 18th, 2017 03:11 PM 
Cantor's Diagonal Argument and Binary Sequences  zylo  Topology  6  May 23rd, 2016 06:57 PM 
Real Number as Binary Sequence  zylo  Topology  8  April 8th, 2016 08:19 PM 
Cantor's Diagonal Sequence is in the list  zylo  Topology  10  March 8th, 2016 02:16 PM 
help with the calculus of infinite sequence  1210  Real Analysis  3  September 20th, 2007 08:06 AM 