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16 replies to this topic

#11 jim

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Posted 05 July 2012 - 03:53 PM

If x=0.999... and y=1.000... then x, if it exists, is a number that differs from a finite sequence of 0.99...99 by an amount that is smaller than any positive number if we carry the expansion out far enough. For example, it will be less than one millionth if we go out 7 decimal places or more. The difference y-x, if it exists, is an approximation for 0.00...001 that has an error that can be made smaller than any positive nuimber if we go to a large enough number of decimal places This is the definition in standard math.

If you wanted to define two real numbers as equal only if the rational approximations used to define the numbers were eventually identical you could do so and get two distinct numbers infinitesimally close together--but that is not the definition that is used in standard math.
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#12 Yoruichi-san

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Posted 05 July 2012 - 06:31 PM

This is getting surreal...

...or perhaps you're trying to push us to our limits ;P

(On a totally unrelated and being a smart@z note in answer to the OP...scientific notation, anyone? :P)
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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

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#13 ujjagrawal

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Posted 06 July 2012 - 06:38 AM

Spoiler for a discussion of almost

Spoiler for My Point...

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#14 bonanova

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Posted 06 July 2012 - 07:48 AM

Spoiler for My point



Spoiler for Precisely

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#15 bonanova

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Posted 06 July 2012 - 08:15 AM

If x=0.999... and y=1.000... then x, if it exists, is a number that differs from a finite sequence of 0.99...99 by an amount that is smaller than any positive number if we carry the expansion out far enough. For example, it will be less than one millionth if we go out 7 decimal places or more. The difference y-x, if it exists, is an approximation for 0.00...001 that has an error that can be made smaller than any positive nuimber if we go to a large enough number of decimal places This is the definition in standard math.

If you wanted to define two real numbers as equal only if the rational approximations used to define the numbers were eventually identical you could do so and get two distinct numbers infinitesimally close together--but that is not the definition that is used in standard math.


Spoiler for Jim

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#16 EventHorizon

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Posted 06 July 2012 - 11:00 PM

Spoiler for Just some musings

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#17 Yoruichi-san

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Posted 06 July 2012 - 11:09 PM

Spoiler for Just some musings


You should also take a look at surreal numbers, which is somewhat related. It's a notation that involves taking the numbers "between" other numbers and is a very interesting way of looking at infinitesimals ^_^ .
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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.




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