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 February 20th, 2018, 09:54 AM #1 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 124 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
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Quote:
 Originally Posted by zylo REAL NUMBERs are defined uniquely by "infinite" (unending) sequences of natural numbers. The sequence IS the real number.
Not sure what you mean... What real number would the sequence
1,2,3,4,5,6,...
correspond to?

 February 20th, 2018, 12:00 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,599 Thanks: 2587 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: 7,912 Thanks: 1110 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. Thanks from Denis, topsquark, v8archie and 1 others
 February 21st, 2018, 10:00 AM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,912 Thanks: 1110 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. The tone must be congenial Those responding must not be ignored All replies must be clearly directed. If you are referring to another thread/statement you must provide a direct link to that thread and that statement Thanks from topsquark
February 21st, 2018, 10:07 AM   #6
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Quote:
 Originally Posted by zylo 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.
How is zero defined by an infinite series of natural number?

 February 21st, 2018, 12:48 PM #7 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 124 0=.000000000...................................... ...
 February 21st, 2018, 02:03 PM #8 Global Moderator   Joined: Dec 2006 Posts: 20,269 Thanks: 1958 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: 13,947 Thanks: 987 Seriously, if we all agree that n-n = .00000000000000....... what has been accomplished?
February 21st, 2018, 06:19 PM   #10
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Quote:
 Originally Posted by zylo REAL NUMBERs are defined uniquely by "infinite" (unending) sequences of natural numbers.
This, on the face of it, claims that $0.999\ldots \ne 1.000\ldots$. Presumably this is an extension of the usual failure to grasp the difference between "infinte" and "arbitrarily large".

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