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2022-01-17, 03:14 PM (ISO 8601)
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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"If you want to understand biology don't think about vibrant throbbing gels and oozes, think about information technology" -Richard Dawkins
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2022-01-17, 03:29 PM (ISO 8601)
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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.
Number of times Roland St. Jude has sworn revenge upon me: 2
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2022-01-17, 04:57 PM (ISO 8601)
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Re: A more concise and intuitive demonstration that 0.9999...=1
Last edited by halfeye; 2022-01-17 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.
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2022-01-17, 06:23 PM (ISO 8601)
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- Feb 2016
Re: A more concise and intuitive demonstration that 0.9999...=1
"If you want to understand biology don't think about vibrant throbbing gels and oozes, think about information technology" -Richard Dawkins
Omegaupdate Forum
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PostImage, a free and sensible alternative to Photobucket
Temple+ Modding Project for Atari's Temple of Elemental Evil
Morrus' RPG Forum (EN World v2)
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2022-01-17, 08:08 PM (ISO 8601)
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Re: A more concise and intuitive demonstration that 0.9999...=1
I made a webcomic, featuring absurdity, terrible art, and alleged morals.
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2022-01-17, 09:23 PM (ISO 8601)
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- 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
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2022-01-17, 10:24 PM (ISO 8601)
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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?Spoiler: I'm a seer
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2022-01-17, 10:58 PM (ISO 8601)
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2022-01-25, 01:46 AM (ISO 8601)
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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"
~Director Cedrik - OotS #640
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2022-01-25, 09:02 AM (ISO 8601)
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- 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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