My Math Forum Cantor's Infinite Binary Sequence

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March 3rd, 2018, 02:31 PM   #11
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Quote:
 Originally Posted by AplanisTophet I decided to browse last night and there you were making the same old arguments yet again.
Hey Aplanis, Nice to see you again. Let's talk about $\mathbb R / \mathbb Q$ sometime!

 March 3rd, 2018, 02:33 PM #12 Global Moderator   Joined: Dec 2006 Posts: 20,302 Thanks: 1971 Your original post in this thread, zylo, refers to a limit that isn't defined properly. If you manage to define it, why is it a list? Last edited by skipjack; March 3rd, 2018 at 02:35 PM.
March 3rd, 2018, 02:57 PM   #13
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Quote:
 Originally Posted by zylo 0 0 0 1 numerical value 2^0 0 0 1 0 numerical value 2^1 0 1 0 0 numerical value 2^2 1 0 0 0 numerical value 2^3, no matter, in general, how many zeros precede the first 1.
Since we can agree that leading zeros can be ignored: how do you differentiate between 11…11, 011…11, 0011…11, etc. each of which appear in your limiting case?

Since each has the same infinite number of 1s, they seem to be equal. And thus you claim that the natural numbers are not unique.

Last edited by v8archie; March 3rd, 2018 at 02:59 PM.

March 5th, 2018, 06:05 AM   #14
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Quote:
 Originally Posted by v8archie Since we can agree that leading zeros can be ignored: how do you differentiate between 11…11, 011…11, 0011…11, etc. each of which appear in your limiting case? Since each has the same infinite number of 1s, they seem to be equal. And thus you claim that the natural numbers are not unique.
It's the sequence that's unique. 0001 and 0010 have the same number of one's.

1111 is not the same as 0111. Again and again and again you are confusing representation with interpretation. Interpretation is irrelevant to OP. You asked for one, so I tried to accomodate you.

Quote:
 Originally Posted by skipjack Your original post in this thread, zylo, refers to a limit that isn't defined properly. If you manage to define it, why is it a list?
If I have defined it for all n I have defined it for the limit as n approaches infinity: an unending sequence of digits where every digit is defined. .333333333333......... for example, WHICH IS NOT 1/3. That is YOUR interpretation of limit, not the one defined in OP,

Last edited by skipjack; March 9th, 2018 at 11:03 AM.

 March 5th, 2018, 08:27 AM #15 Global Moderator   Joined: Dec 2006 Posts: 20,302 Thanks: 1971 Why is it a list? Referring to it as a list doesn't imply that it is a list.
March 5th, 2018, 08:28 AM   #16
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Quote:
 Originally Posted by zylo It's the sequence that's unique. 0001 and 0010 have the same number of one's. 1111 is not the same as 0111. Again and again and again you are confusing representation with interpretation. Interpretation is irrelevant to OP. You asked for one, so I tried to accomodate you.
Why are you talking about $n=4$? I explicitly said I was talking about the limiting case in which there are an infinite number of elements.

March 5th, 2018, 08:53 AM   #17
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Quote:
 Originally Posted by zylo Interpretation is irrelevant to OP. You asked for one, so I tried to accomodate you.
No I didn't. I asked what the second element of you list is. You chose to give an interpretation, so I used that interpretation to ask you about other elements.

You know that you are making this all up, so you are deliberately obfuscating in an attempt to hide the fact that what you hope to show is wrong.

March 5th, 2018, 09:59 AM   #18
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Quote:
 Originally Posted by skipjack Why is it a list? Referring to it as a list doesn't imply that it is a list.
Look at it.

EDIT
v8archie. I simply observed that you could associate a natural number with every member of the list, which puts it in numerical order, for all n.

I acknowledge your opinion that for all n doesn't include infinity.

Last edited by zylo; March 5th, 2018 at 10:13 AM.

 March 5th, 2018, 10:57 AM #19 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,600 Thanks: 2588 Math Focus: Mainly analysis and algebra Perhaps you could try answering the questions I asked then instead of continually deflecting. You can start with: what is the second entry in the limiting case? PS: it's not an opinion that for all $n$ doesn't include "infinity", it's a fact.
March 5th, 2018, 11:40 AM   #20
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Quote:
 Originally Posted by v8archie Perhaps you could try answering the questions I asked then instead of continually deflecting.

 Tags binary, cantor, infinite, sequence

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