My Math Forum > Math Are the decimal real numbers a field.

 Math General Math Forum - For general math related discussion and news

 January 18th, 2019, 09:59 AM #1 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 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: 884
Thanks: 340

Quote:
 Originally Posted by zylo 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?

January 18th, 2019, 10:53 AM   #3
Banned Camp

Joined: Mar 2015
From: New Jersey

Posts: 1,720
Thanks: 126

Quote:
 Originally Posted by Micrm@ss 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.

 January 18th, 2019, 11:34 AM #4 Senior Member   Joined: Jun 2014 From: USA Posts: 617 Thanks: 50 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: 126

Quote:
 Originally Posted by AplanisTophet I'm just going to say "no" on this one. I trust that suffices as an answer.
Thank goodness. Is that a promise?

 January 18th, 2019, 03:06 PM #6 Global Moderator   Joined: Dec 2006 Posts: 21,027 Thanks: 2258 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

 Tags decimal, field, numbers, real

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post prashantakerkar Calculus 1 March 21st, 2017 11:20 PM zylo Topology 20 July 19th, 2016 06:44 PM Pengkuan Math 8 March 13th, 2016 04:38 AM crystalnaidoo Math 3 April 29th, 2015 06:46 PM zolden Number Theory 1 December 11th, 2008 08:14 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top