February 20th, 2018, 09:54 AM  #1 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,603 Thanks: 115  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, 10:23 AM  #2 
Senior Member Joined: Oct 2009 Posts: 630 Thanks: 193  
February 20th, 2018, 12:00 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,512 Thanks: 2514 Math Focus: Mainly analysis and algebra 
Good luck, Micrm@ss.

February 20th, 2018, 12:09 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,885 Thanks: 1088 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, 10:00 AM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,885 Thanks: 1088 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, 10:07 AM  #6 
Senior Member Joined: May 2016 From: USA Posts: 1,210 Thanks: 497  
February 21st, 2018, 12:48 PM  #7 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,603 Thanks: 115 
0=.000000000...................................... ...

February 21st, 2018, 02:03 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 19,985 Thanks: 1853 
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, 02:08 PM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,629 Thanks: 954 
Seriously, if we all agree that nn = .00000000000000....... what has been accomplished? 
February 21st, 2018, 06:19 PM  #10  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,512 Thanks: 2514 Math Focus: Mainly analysis and algebra  Quote:
Do we really need another thread about that?  

Tags 
limits, numbers, real 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Real Numbers and Natural Numbers  zylo  Topology  14  May 10th, 2017 02:57 AM 
Dimensions, and numbers beyond real numbers  Elektron  Math  4  May 7th, 2017 12:47 PM 
Real Analysis: Numerical Sequences (limits)  Luiz  Real Analysis  3  March 23rd, 2015 08:08 AM 
Real Analysis: Numerical Sequences (limits)  Luiz  Real Analysis  1  March 18th, 2015 09:39 AM 
Let a,b be real numbers such that....  thehurtlooker  Algebra  3  April 9th, 2013 01:58 AM 