My Math Forum Cantor's Infinite Binary Sequence

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March 5th, 2018, 11:08 AM   #21
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Quote:
 Originally Posted by v8archie And so, again: what is 100…000 in your limiting case? How do you write it as a power of 2? ..........................
Again, 100...000 in the limiting case is 1 followed by an endless number of zeros.

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
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Quote:
 Originally Posted by greg1313 Please provide direct references.
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
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Quote:
 Originally Posted by zylo Look at it.
It's not obvious to me. Can you prove it's a list?

March 5th, 2018, 05:04 PM   #24
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Quote:
 Originally Posted by v8archie 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.
I asked you to provide direct references, not to make a list of excuses as to why you shouldn't have to do that. When I said this (and similar treads, n.b.) will be strictly moderated, I meant they will be strictly moderated. There's no point in continuing this discussion if the rules I laid out aren't goint to be followed. This time, I am willing to let it slide but, in future, please provide direct references, no matter how clear you think the implications of your post are. Thank you.

@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
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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:
 Originally Posted by v8archie In the limiting case, what do you think the second element in your list is?
Since Zylo says that the limiting case consists of a list of infinite sequences of binary digits and is a representation to which we should ascribe an interpretation, I expect the answer to be something like
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 ill-defined 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
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Quote:
 Originally Posted by zylo Therefore I will start a new thread with what I intended to post here.
Like some girl said to me in high school: Let's not and say we did.

March 9th, 2018, 08:51 AM   #28
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Quote:
 Originally Posted by v8archie In the limiting case, what do you think the second element in your list is?
answered in posts #4 and 7.

 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?

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