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20220117, 03:14 PM (ISO 8601)
 Join Date
 Feb 2016
A more concise and intuitive demonstration that 0.9999...=1
Most of the explanations I've seen of why 0.999...repeating equals 1.0 have seemed a little esoteric, but I just thought of a really simple demonstration showing that they're equal
Start with the number 1.1111....repeating
Subtract 1 (leaving you with 0.1111...repeating)
add 0.9999....repeating
and you see immediately that it gives you back the original number"we do not say anything in it, unless it is worth taking a long time to say, and to listen to" Treebeard
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20220117, 03:29 PM (ISO 8601)
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 Dec 2009
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 Birmingham, AL
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Re: A more concise and intuitive demonstration that 0.9999...=1
Esoteric?
0.333.... = 1/3.
3 x 1/3 = 1, so 3 x 0.333.... = 1, so 0.999.... = 1.
What's esoteric about that?Cuthalion's art is the prettiest art of all the art. Like my avatar.
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20220117, 04:57 PM (ISO 8601)
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 Jun 2013
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 Bristol, UK
Re: A more concise and intuitive demonstration that 0.9999...=1
Last edited by halfeye; 20220117 at 05:00 PM.
The end of what Son? The story? There is no end. There's just the point where the storytellers stop talking.

20220117, 06:23 PM (ISO 8601)
 Join Date
 Feb 2016
Re: A more concise and intuitive demonstration that 0.9999...=1
"we do not say anything in it, unless it is worth taking a long time to say, and to listen to" Treebeard
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20220117, 08:08 PM (ISO 8601)
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 Feb 2016
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 Earth and/or notEarth
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Re: A more concise and intuitive demonstration that 0.9999...=1
I'm making a webcomic, featuring absurdity, terrible art, and alleged morals.

20220117, 09:23 PM (ISO 8601)
 Join Date
 Aug 2011
Re: A more concise and intuitive demonstration that 0.9999...=1
From what I can tell, proving that 0.9999... + 0.1111.... = 1.1111.... requires*** some way of working with sums of infinite geometric series, and if you can do that it's more straight forward to just directly prove that 0.9999... = 1.
***Maybe it doesn't but I suspect other methods would be even more esotericOriginally Posted by crayzzOriginally Posted by jere7my

20220117, 10:24 PM (ISO 8601)
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 May 2014
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 Germany
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Re: A more concise and intuitive demonstration that 0.9999...=1
(X × 10  X)/9 = X
Correct?
Now use 0.9999... for X
0.9999... × 10 = 9.9999...
9.9999...  0.9999 = 9
9 / 9 = 1
Simple, right?

20220117, 10:58 PM (ISO 8601)
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 Dec 2009
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 Birmingham, AL
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20220125, 01:46 AM (ISO 8601)
 Join Date
 May 2013
 Location
 southeastern USA
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Re: A more concise and intuitive demonstration that 0.9999...=1
"A good way to get a decent person to do something horrible is to convince them that they're not responsible for their actions"
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20220125, 09:02 AM (ISO 8601)
 Join Date
 Aug 2007
Re: A more concise and intuitive demonstration that 0.9999...=1
Between any two distinct numbers, there are infinite other numbers. (e.g. between 1.3 and 1.4 is 1.31, 1.32, 1.34593875834754985398475, etc)
If .999... does not equal 1, you should be able to name at lest one of the numbers in between.
You can't, therefore they must be the same number, written in two different ways.
Nothing esoteric about that, I feel.
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