My Math Forum Is an Infinite Binary Sequence a Natural Number?

 Real Analysis Real Analysis Math Forum

 July 18th, 2017, 04:22 AM #41 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 Two binary-digit natural numbers: 00 -> 0 01 -> 1 10 -> 2 11 -> 3 Three binary-digit natural numbers: 000 -> 0 001 -> 1 010 -> 2 011 -> 3 100 -> 4 101 -> 5 110 -> 6 111 -> 7 Infinite binary-digit natural numbers (Infinite Binary Sequences): ....00000 -> 0 ....00001 -> 1 ....00010 -> 2 ....00011 -> 3 ....00100 -> 4 ....00101 -> 5 ....00110 -> 6 ....00111 -> 7 ............ ............ Preceding zeros conventionally not displayed or indicated.
July 18th, 2017, 04:29 AM   #42
Senior Member

Joined: Oct 2009

Posts: 884
Thanks: 340

Quote:
 Originally Posted by zylo Two binary-digit natural numbers: 00 -> 0 01 -> 1 10 -> 2 11 -> 3 Three binary-digit natural numbers: 000 -> 0 001 -> 1 010 -> 2 011 -> 3 100 -> 4 101 -> 5 110 -> 6 111 -> 7 Infinite binary-digit natural numbers (Infinite Binary Sequences): ....00000 -> 0 ....00001 -> 1 ....00010 -> 2 ....00011 -> 3 ....00100 -> 4 ....00101 -> 5 ....00110 -> 6 ....00111 -> 7 ............ ............ Preceding zeros conventionally not displayed or indicated.
Cool, so what is the decimal notation of ...1111111 ?
And what would be ...111111 + 1?

July 18th, 2017, 04:30 AM   #43
Senior Member

Joined: Oct 2009

Posts: 884
Thanks: 340

Quote:
 Originally Posted by zylo Two binary-digit natural numbers: 00 -> 0 01 -> 1 10 -> 2 11 -> 3 Three binary-digit natural numbers: 000 -> 0 001 -> 1 010 -> 2 011 -> 3 100 -> 4 101 -> 5 110 -> 6 111 -> 7 Infinite binary-digit natural numbers (Infinite Binary Sequences): ....00000 -> 0 ....00001 -> 1 ....00010 -> 2 ....00011 -> 3 ....00100 -> 4 ....00101 -> 5 ....00110 -> 6 ....00111 -> 7 ............ ............ Preceding zeros conventionally not displayed or indicated.
Also, are you not going to provide the definitions that I asked for?

July 18th, 2017, 07:59 AM   #44
Senior Member

Joined: Jun 2014
From: USA

Posts: 617
Thanks: 50

Quote:
 Originally Posted by zylo Infinite binary-digit natural numbers (Infinite Binary Sequences): ....00000 -> 0 ....00001 -> 1 ....00010 -> 2 ....00011 -> 3 ....00100 -> 4 ....00101 -> 5 ....00110 -> 6 ....00111 -> 7 ............ ............ Preceding zeros conventionally not displayed or indicated.
All of the infinite binary sequences in your list contain a finite number of 1's. No sequences containing an infinite number of 1's are included. Therefore, you've only managed to produce a bijection between a small subset of the infinite binary sequences and the natural numbers.

I realize you think that all of the infinite binary sequences appear in your list, as that is what you assert time and time again. You are flapping your arms as though you are convinced you can fly. Move on.

 July 18th, 2017, 08:55 AM #45 Global Moderator   Joined: Dec 2006 Posts: 21,027 Thanks: 2258 If you write the "infinite" sequences that way round, zylo, CDA is still applicable if you start the diagonal at the top right instead of the top left.
 July 18th, 2017, 03:11 PM #46 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra Since Zylo believes that his list goes $$\begin{gather}000\ldots000 \\ 000\ldots001 \\ 000\ldots010 \\ \vdots \\111\ldots111\end{gather}$$This means that the first few have finite quantities of $1$s and the last few have infinite quantities of $1$s. A pertinent question is: when do we make the transition from finite $1$s to infinite $1$s?

 Tags binary, blah, infinite, natural, number, sequence

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post zylo Topology 25 June 4th, 2016 11:55 PM zylo Topology 8 April 8th, 2016 08:19 PM Zman15 Elementary Math 10 March 28th, 2015 06:42 AM Shen Elementary Math 2 June 5th, 2014 07:50 AM durky Abstract Algebra 1 March 15th, 2012 11:28 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top