July 18th, 2017, 04:22 AM  #41 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,400 Thanks: 100 
Two binarydigit natural numbers: 00 > 0 01 > 1 10 > 2 11 > 3 Three binarydigit natural numbers: 000 > 0 001 > 1 010 > 2 011 > 3 100 > 4 101 > 5 110 > 6 111 > 7 Infinite binarydigit 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: 436 Thanks: 147  Quote:
And what would be ...111111 + 1?  
July 18th, 2017, 04:30 AM  #43  
Senior Member Joined: Oct 2009 Posts: 436 Thanks: 147  Quote:
 
July 18th, 2017, 07:59 AM  #44  
Senior Member Joined: Jun 2014 From: USA Posts: 364 Thanks: 26  Quote:
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: 19,295 Thanks: 1686 
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: 7,344 Thanks: 2466 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  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Infinite Decimal is a Natural Number  zylo  Topology  25  June 4th, 2016 11:55 PM 
Real Number as Binary Sequence  zylo  Topology  8  April 8th, 2016 08:19 PM 
binary number system  Zman15  Elementary Math  10  March 28th, 2015 06:42 AM 
natural number multiple of another number if its digit sum equal to that number  Shen  Elementary Math  2  June 5th, 2014 07:50 AM 
Infinite set contains an infinite number of subsets  durky  Abstract Algebra  1  March 15th, 2012 11:28 AM 