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 June 7th, 2014, 04:25 AM #1 Newbie   Joined: Apr 2014 From: USA Posts: 24 Thanks: 1 rational number Can you give me an example of an infinite decimal RATIONAL number formed by natural numbers used just once? It should be of the form ( 0,..............) .
 June 7th, 2014, 04:42 AM #2 Senior Member     Joined: Apr 2014 From: zagreb, croatia Posts: 234 Thanks: 33 Math Focus: philosophy/found of math, metamath, logic, set/category/order/number theory, algebra, topology 0,3333333
 June 7th, 2014, 12:25 PM #3 Newbie   Joined: Jun 2014 From: Princeton wv Posts: 4 Thanks: 0 What am I missing? Definition: " a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero." Wy does 1/3 not qualify?
June 7th, 2014, 01:08 PM   #4
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Quote:
 Originally Posted by randyg45 Definition: " a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero." Wy does 1/3 not qualify?
It does.

 June 7th, 2014, 04:42 PM #5 Member   Joined: Feb 2012 From: Hastings, England Posts: 83 Thanks: 14 Math Focus: Problem Solving there's quite a few surely, 1/9 is another?
June 7th, 2014, 07:22 PM   #6
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Quote:
 Originally Posted by nmenumber1 there's quite a few surely, 1/9 is another?
Yes. 0.11111111111111111111

2/3 = 0.66666666666

June 8th, 2014, 03:31 PM   #7
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Quote:
 Originally Posted by Roli Can you give me an example of an infinite decimal RATIONAL number formed by natural numbers used just once? It should be of the form ( 0,..............) .
Did you mean using only one integer repeated or something else?

All the answers are for one digit repeated. There are 8 possibilities:

0.nnnnnn........ = n/9 where n is any integer from 1 to 8.

 June 8th, 2014, 05:53 PM #8 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,659 Thanks: 2635 Math Focus: Mainly analysis and algebra I wondered whether it was a request for an infinite decimal expansion in which no natural number is repeated. But any infinite decimal expansion of a rational will do. For example $\frac13 = 0.3\,33\,333\,3333\,33333\,\cdots$ where the spaces are inserted to highlight the natural numbers used.
June 9th, 2014, 05:33 AM   #9
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Quote:
 Originally Posted by Roli Can you give me an example of an infinite decimal RATIONAL number formed by natural numbers used just once? It should be of the form ( 0,..............) .
I think I wasn't clear. It should contain ALL the natural numbers ( as a bijection ) and each natural number should be used ONCE. It can go infinitely or not.
But it must respect a rule.

June 9th, 2014, 05:33 AM   #10
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 Originally Posted by raul21 It does.
I think I wasn't clear. It should contain ALL the natural numbers ( as a bijection ) and each natural number should be used ONCE. It can go infinitely or not.
But it must respect a rule.

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