July 7th, 2018, 01:44 PM  #61 
Global Moderator Joined: Dec 2006 Posts: 19,725 Thanks: 1807 
Can you explain the "stones" method in detail, and how it would let you count 1, 2, 3, 4, ... (continued without end)? In your reference to counting nplace representations, you don't say what exactly are being represented by the nplace representations. Also, "through n approaches infinity" is unclear and possibly grammatically incorrect. You then state "as proved by induction", but you haven't provided such a proof, and it isn't clear what exactly needs to be proved. 
July 9th, 2018, 05:48 AM  #62 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,548 Thanks: 111 
$\displaystyle \lim_{n\rightarrow \infty} .33333 = .333333....... = 3\bar{n}$ $\displaystyle \lim_{n\rightarrow \infty} .33333 = 1/3$ The first limit is a representation limit (point). The second lim is a sum limit which gives the distance of the point from the origin. I can count ALL nplace binaries (or any radix), ie, for n through "infinity." There are two possibilities: You don't like what I mean or you don't understand what I mean. Last edited by zylo; July 9th, 2018 at 06:11 AM. Reason: (decimals 
July 9th, 2018, 07:11 AM  #63 
Global Moderator Joined: Dec 2006 Posts: 19,725 Thanks: 1807 
I don't understand what you mean. That's bound to be the case if you declare "I can", but don't describe your method unambiguously and in detail. Before you try to explain, please answer my questions in my preceding post, so that we can begin to understand what you mean by "count".

July 9th, 2018, 07:30 AM  #64 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,548 Thanks: 111 
00 01 10 11 I have listed all two place binaries. How many are there in the list? 
July 9th, 2018, 08:11 AM  #65 
Global Moderator Joined: Dec 2006 Posts: 19,725 Thanks: 1807 
There are four, but I didn't use stones. Please answer my questions before posting new questions.

July 9th, 2018, 08:23 AM  #66 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,548 Thanks: 111 
As you recall, I used stones as a question, not an answer. If you like, stones are a primitive analogy of the natural numbers. How many buckets of wheat will you give me for my donkey? I show four (4) stones. So you don't bury and distract the thread, I withdraw whatever I said. or you thought I said, about stones. Now how many entries are in the list of all 3place decimals, and how did you get there from the list of all 2place decimals? Last edited by skipjack; July 9th, 2018 at 09:33 AM. 
July 9th, 2018, 09:44 AM  #67  
Senior Member Joined: Oct 2009 Posts: 561 Thanks: 179  Quote:
 
July 9th, 2018, 09:49 AM  #68 
Global Moderator Joined: Dec 2006 Posts: 19,725 Thanks: 1807 
As you've withdrawn your earlier mentions of sticks, stones, scratches on a rock, etc., my earlier question becomes: how would you count 1, 2, 3, 4, ... (continued without end) without a number system? Please answer that question (without using stones, scratches on a rock or the like, of course) before posting any new question.

July 9th, 2018, 09:54 AM  #69 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,548 Thanks: 111  
July 9th, 2018, 09:57 AM  #70  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,548 Thanks: 111  Quote:
 

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