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January 18th, 2019, 10:59 AM   #1
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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
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Quote:
Originally Posted by zylo View Post
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.
Are you talking about zylo's real numbers, or about the real numbers that the rest of the world uses?
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January 18th, 2019, 11:53 AM   #3
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Quote:
Originally Posted by Micrm@ss View Post
Are you talking about zylo's real numbers, or about the real numbers that the rest of the world uses?
The real world hasn't gotten it straight yet.
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January 18th, 2019, 12:34 PM   #4
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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
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Originally Posted by AplanisTophet View Post
I'm just going to say "no" on this one. I trust that suffices as an answer.
Thank goodness. Is that a promise?

Thanks for the complement. I just read your post in "the other" thread.
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January 18th, 2019, 04:06 PM   #6
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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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