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January 18th, 2019, 09:59 AM  #1 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125  Are the decimal real numbers a field.
Is the following decimal definition of real numbers a field?  Defining the natural numbers by decimal digits is trivial: 1, 2, 3, ... One way to define all the real numbers in [0,1) is to list the natural numbers, put a period after them, and read them in reverse. 1. Is .1 2. Is .2 . 10. Is .01 95141. is .14159  It is because you can define closed addition, subtraction, multiplication and division, for any finite decimal, and the decimals are countable. See above. 
January 18th, 2019, 10:32 AM  #2  
Senior Member Joined: Oct 2009 Posts: 784 Thanks: 280  Quote:
 
January 18th, 2019, 10:53 AM  #3 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125  
January 18th, 2019, 11:34 AM  #4 
Senior Member Joined: Jun 2014 From: USA Posts: 525 Thanks: 40 
I'm just going to say "no" on this one. I trust that suffices as an answer.

January 18th, 2019, 11:47 AM  #5 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125  
January 18th, 2019, 03:06 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,644 Thanks: 2084 
You haven't given all the real numbers in [0,1). One can pick an example from anywhere in your list and be certain that it doesn't correspond to 1/9.


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decimal, field, numbers, real 
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