March 7th, 2018, 09:31 AM  #71  
Senior Member Joined: Aug 2012 Posts: 2,134 Thanks: 621  Quote:
You also seem confused about the difference between a sequence and a series. The above is a sequence.  
March 7th, 2018, 09:47 AM  #72 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,559 Thanks: 2558 Math Focus: Mainly analysis and algebra  Zylo also doesn't understand the difference between "unbounded" and "infinite". I don't understand how someone who is so obviously motivated to investigate mathematics can be comfortable being so ignorant about so many basic facts and definitions. Last edited by v8archie; March 7th, 2018 at 09:59 AM. 
March 7th, 2018, 09:53 AM  #73  
Senior Member Joined: Aug 2012 Posts: 2,134 Thanks: 621  Quote:
I would only say that when you write, "If you can make a rationalsounding argument that they are just sequences for which we can always get another element when we need it, the job will be done," you're only restating the problem, not outlining an approach to a solution. But perhaps you've described Goodstein's idea. I have no way to know  
March 7th, 2018, 10:07 AM  #74  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,559 Thanks: 2558 Math Focus: Mainly analysis and algebra  Quote:
I certainly wouldn't suggest that I path to a watertight solution. It really would be restating the existing construction in finitist language. As I say, though, it's interesting how little we appeal to the infinite to create the reals.  
March 7th, 2018, 10:45 AM  #75  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,637 Thanks: 119  Quote:
Quote:
ZFC Axiom of regularity  
March 7th, 2018, 10:46 AM  #76 
Senior Member Joined: Aug 2012 Posts: 2,134 Thanks: 621  That sequence doesn't end. The only kind of sequence that ends is a finite one.

March 7th, 2018, 10:52 AM  #77 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,637 Thanks: 119  
March 7th, 2018, 11:28 AM  #78 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,559 Thanks: 2558 Math Focus: Mainly analysis and algebra  You don't seem able to tell the difference, unless your unbounded/infinite sequence is a third option that terminates after an infinite number of terms. (That third option is nonsense, by the way  I thought I'd better say so to avoid confusing you.)

March 8th, 2018, 03:15 AM  #79 
Global Moderator Joined: Dec 2006 Posts: 20,101 Thanks: 1905  By that reasoning, if S_n is defined to be n for all n, and "finite length" is replaced by "finite", you would be asserting that though some values of n are finite, n isn't finite for every n. For what value of n wouldn't n be finite?


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