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February 20th, 2018, 08:54 AM   #1
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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.
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February 20th, 2018, 09:23 AM   #2
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Quote:
Originally Posted by zylo View Post
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?
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February 20th, 2018, 11:00 AM   #3
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Good luck, Micrm@ss.
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February 20th, 2018, 11:09 AM   #4
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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.
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February 21st, 2018, 09:00 AM   #5
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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
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February 21st, 2018, 09:07 AM   #6
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Quote:
Originally Posted by zylo View Post
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?
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February 21st, 2018, 11:48 AM   #7
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0=.000000000...................................... ...
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February 21st, 2018, 01:03 PM   #8
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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.
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February 21st, 2018, 01:08 PM   #9
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Seriously, if we all agree that n-n = .00000000000000.......
what has been accomplished?
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February 21st, 2018, 05:19 PM   #10
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Quote:
Originally Posted by zylo View Post
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".

Do we really need another thread about that?
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