January 16th, 2019, 08:03 AM  #1 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125  Real numbers and decimals.
All real numbers can be defined by unique decimal sequences unrestricted in length. Convergence in the conventional sense has nothing to do with this. Addition and multiplication of two endless sequences is a problem because it starts from the right, but there are practical workarounds which satisfy all the requirements of science and engineering. If you replace decimal definition with abstract definitions, you regress to people living in caves with rulers who scratch symbols on the walls. Sequences: Example: 1352976....., .1352976...... 
January 16th, 2019, 08:05 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  
January 16th, 2019, 08:36 AM  #3 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125  
January 16th, 2019, 08:46 AM  #4 
Senior Member Joined: Aug 2012 Posts: 2,311 Thanks: 706  
January 16th, 2019, 08:48 AM  #5  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
Your real numbers can be defined by unique decimal sequences unrestricted in length. OK. I have no interest in your real numbers.  
January 16th, 2019, 08:54 AM  #6 
Senior Member Joined: Dec 2015 From: somewhere Posts: 514 Thanks: 80 
At least show one counterexample if possible. If not then prove it. Last edited by idontknow; January 16th, 2019 at 08:58 AM. 
January 16th, 2019, 08:57 AM  #7 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125 
Maschke. Please give "Counter example" {whatever that means} JeffM1. Please give your definition of a real number and a representative member, other than "x" or "a." EDIT I wavered between "represented by" and "defined by". But what is it you are representing? A Dedekind cut? How do you define a Dedekind cut without numbers, and then what decimal do you assign to it? Last edited by skipjack; January 16th, 2019 at 01:57 PM. 
January 16th, 2019, 10:14 AM  #8 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 
A representative real number is 1. According to you it has a unique decimal representation. Prove it. You are the one trying to demonstrate something. I am under no obligation to do anything. I accept that you may define things as you please, but then what you have to say has no relevance to anyone else. 
January 16th, 2019, 10:29 AM  #9 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125 
1 is a real number by definition: it is a unique decimal sequence. "No relevance to anyone else?" You mean to you, don't you? Last edited by skipjack; January 16th, 2019 at 01:58 PM. 
January 16th, 2019, 10:42 AM  #10 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  

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decimals, numbers, real 
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