Are the decimal real numbers a field.

zylo · January 18th, 2019, 10:59 AM

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.

Micrm@ss · January 18th, 2019, 11:32 AM

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?

zylo · January 18th, 2019, 11:53 AM

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.

AplanisTophet · January 18th, 2019, 12:34 PM

I'm just going to say "no" on this one. I trust that suffices as an answer.

zylo · January 18th, 2019, 12:47 PM

Quote:

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.

skipjack · January 18th, 2019, 04:06 PM

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.

January 18th, 2019, 10:59 AM	#1
zylo 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.
$zylo is offline$

January 18th, 2019, 12:34 PM	#4
AplanisTophet 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.
$AplanisTophet is offline$

January 18th, 2019, 04:06 PM	#6
skipjack 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. Thanks from topsquark
$skipjack is offline$

Thread Tools
$Show Printable Version$ Show Printable Version $Email this Page$ Email this Page
Display Modes
$Linear Mode$ Linear Mode $Hybrid Mode$ Switch to Hybrid Mode $Threaded Mode$ Switch to Threaded Mode

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Matrix having Decimal numbers.	prashantakerkar	Calculus	1	March 22nd, 2017 12:20 AM
Ordering of real numbers and decimal fractions	zylo	Topology	20	July 19th, 2016 07:44 PM
Cardinality of the set of decimal numbers	Pengkuan	Math	8	March 13th, 2016 05:38 AM
decimal numbers	crystalnaidoo	Math	3	April 29th, 2015 07:46 PM
Sum of decimal numbers	zolden	Number Theory	1	December 11th, 2008 09:14 PM