February 20th, 2018, 08:54 AM  #1 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,300 Thanks: 94  Real Numbers and Limits
REAL NUMBERs are defined uniquely by "infinite" (unending) sequences of natural numbers. The sequence IS the real number. LIMIT is a defined property of real numbers. 
February 20th, 2018, 09:23 AM  #2 
Senior Member Joined: Oct 2009 Posts: 275 Thanks: 92  
February 20th, 2018, 11:00 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,236 Thanks: 2412 Math Focus: Mainly analysis and algebra 
Good luck, Micrm@ss.

February 20th, 2018, 11:09 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,767 Thanks: 1016 Math Focus: Elementary mathematics and beyond 
This topic has been discussed numerous times in numerous threads, so I'll spare us all by closing this thread. Search zylo's posts and respond there if you wish to continue the discussion.

February 21st, 2018, 09:00 AM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,767 Thanks: 1016 Math Focus: Elementary mathematics and beyond 
Alright, I've reopened the thread. Please be advised that the following rules must be followed when participating in the discussion  if you can't abide by them, don't post.

February 21st, 2018, 09:07 AM  #6 
Senior Member Joined: May 2016 From: USA Posts: 923 Thanks: 369  
February 21st, 2018, 11:48 AM  #7 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,300 Thanks: 94 
0=.000000000...................................... ...

February 21st, 2018, 01:03 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 18,716 Thanks: 1532 
One might as well omit trailing zeros and also omit the decimal separator for integers, so that zero can be written as just 0. For uniqueness, it would also be necessary to write 2.19999..., say, as 2.2, which adds a bit of inelegance to the definition.

February 21st, 2018, 01:08 PM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,858 Thanks: 768 
Seriously, if we all agree that nn = .00000000000000....... what has been accomplished? 
February 21st, 2018, 05:19 PM  #10  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,236 Thanks: 2412 Math Focus: Mainly analysis and algebra  Quote:
Do we really need another thread about that?  

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