July 18th, 2017, 04:22 AM  #41 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,364 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: 406 Thanks: 141  Quote:
And what would be ...111111 + 1?  
July 18th, 2017, 04:30 AM  #43  
Senior Member Joined: Oct 2009 Posts: 406 Thanks: 141  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: 19,065 Thanks: 1621 
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: 7,313 Thanks: 2447 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?


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binary, blah, infinite, natural, number, sequence 
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