My Math Forum An Anomaly of Decimal Representation

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 July 7th, 2018, 01:44 PM #61 Global Moderator   Joined: Dec 2006 Posts: 20,937 Thanks: 2210 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 n-place representations, you don't say what exactly are being represented by the n-place 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 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 $\displaystyle \lim_{n\rightarrow \infty} .33333 = .333333....... = 3\bar{n}$ $\displaystyle \lim_{n\rightarrow \infty} .33333 = 1/3$ 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 n-place 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: 20,937 Thanks: 2210 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 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 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: 20,937 Thanks: 2210 There are four, but I didn't use stones. Please answer my questions before posting new questions.
 July 9th, 2018, 08:23 AM #66 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 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 3-place decimals, and how did you get there from the list of all 2-place decimals? Last edited by skipjack; July 9th, 2018 at 09:33 AM.
July 9th, 2018, 09:44 AM   #67
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 Originally Posted by zylo 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 3-place decimals, and how did you get there from the list of all 2-place decimals?
8, and I get it by duplicating the 2 place decimal list, and adding 0 to one list, and 1 to the other. What's the point?

 July 9th, 2018, 09:49 AM #68 Global Moderator   Joined: Dec 2006 Posts: 20,937 Thanks: 2210 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
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 Originally Posted by Micrm@ss 8, and I get it by duplicating the 2 place decimal list, and adding 0 to one list, and 1 to the other. What's the point?
Induction as a means to specify and count all "infinite" place decimals (binaries, radixes). Points on a line.

July 9th, 2018, 09:57 AM   #70
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 Originally Posted by skipjack 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.
1,2,3,4,.... are the count.

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