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January 18th, 2019, 10:59 AM | #1 |
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 124 | 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. |
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January 18th, 2019, 11:32 AM | #2 | |
Senior Member Joined: Oct 2009 Posts: 733 Thanks: 247 | Quote:
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January 18th, 2019, 11:53 AM | #3 |
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 124 | |
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January 18th, 2019, 12:34 PM | #4 |
Senior Member Joined: Jun 2014 From: USA Posts: 479 Thanks: 36 |
I'm just going to say "no" on this one. I trust that suffices as an answer.
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January 18th, 2019, 12:47 PM | #5 |
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 124 | |
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January 18th, 2019, 04:06 PM | #6 |
Global Moderator Joined: Dec 2006 Posts: 20,298 Thanks: 1971 |
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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