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jadesmar
Bad Puppy
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 Posted: Thu Feb 14, 2013 3:34 am Post subject: 121 |
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| MNOWAX wrote: |
I will do one thing to add to this conversation, since I was the .99999... of the troll that I am.
1/3*3=1
1/3=.33333....
.33333...* 3 = 1
.99999...=1
Disprove that. |
Obviously the bit that claims
1/3=0.333... Is just an approximation. |
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LordKinbote
Daedalian Member
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| Posted: Thu Feb 14, 2013 4:07 am Post subject: 122 |
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| jadesmar wrote: |
Obviously the bit that claims
1/3=0.333... Is just an approximation. |
And it's off by...how much, exactly? |
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MNOWAX
0.999... of a Troll
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| Posted: Thu Feb 14, 2013 4:49 am Post subject: 123 |
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| jadesmar wrote: |
Obviously the bit that claims
1/3=0.333... Is just an approximation. |
but...it's not. Go ahead, divide one into three. Do the long division. I'l wait. You'll eventually get bored too.
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The Man The Myth The Legend
MNOWAX |
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referee
June 21st, 2004 Member
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| Posted: Thu Feb 14, 2013 5:01 am Post subject: 124 |
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| MNOWAX wrote: |
| Do the long division. |
Understatement of History.
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Jan 21st, 2008: The pillaging continues.
Mar 4th, 2008: Rest in Peace, Gary Gygax. May your dice always roll a natural 20 wherever you are.
Be the Ultimate Ninja! Play Billy Vs. SNAKEMAN today! |
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extropalopakettle
No offense, but....
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| Posted: Thu Feb 14, 2013 9:34 am Post subject: 125 |
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| LordKinbote wrote: |
| jadesmar wrote: |
Obviously the bit that claims
1/3=0.333... Is just an approximation. |
And it's off by...how much, exactly? |
I would imagine taking 1/3 - 0.333... would, according to DM's theory, present the same problem as taking 1 - 0.999...
The problem being, that while 0.999... is the largest number less than 1, and 0.333... is the largest number less than 1/3, when you try to do subtraction or other operations with these numbers, they cease to be numbers and transform into infinite strings (though somehow remaining comparable to ordinary numbers with "less than" and "greater than"). |
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extropalopakettle
No offense, but....
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| Posted: Thu Feb 14, 2013 9:46 am Post subject: 126 |
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Otherwise:
Let X = 1/3 - 0.333...
Then:
3X = 1 - 0.999 ...
Adding 0.999... to both sides:
0.999... + 3X = 1
Then:
0.999 ... < 0.999... + X < 0.999... + 3X = 1
Which contradicts that 0.999... is the largest number less than 1.
(I carefully avoided attempting to divide the number 1-0.999... by anything to obtain X, as then it would use its superpowers to transform into an infinite string to protect itself from division) |
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LordKinbote
Daedalian Member
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| Posted: Thu Feb 14, 2013 12:59 pm Post subject: 127 |
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| extropalopakettle wrote: |
Otherwise:
Let X = 1/3 - 0.333...
Then:
3X = 1 - 0.999 ...
Adding 0.999... to both sides:
0.999... + 3X = 1
Then:
0.999 ... < 0.999... + X < 0.999... + 3X = 1
Which contradicts that 0.999... is the largest number less than 1.
(I carefully avoided attempting to divide the number 1-0.999... by anything to obtain X, as then it would use its superpowers to transform into an infinite string to protect itself from division) |
I'm glad you posted this because I was about to post pretty much the same thing in less formal terms: "If .333... is off by the smallest possible amount, then wouldn't .999 be off by the smallest possible amount which just happens to be three times larger than that other amount?" |
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extropalopakettle
No offense, but....
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| Posted: Thu Feb 14, 2013 1:11 pm Post subject: 128 |
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| I'm picturing some xkcd style comic where 0.999... transforms back and forth between number and infinite string whenever threatened by mathematical operations. |
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Jedo the Jedi
Paragon in Training
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| Posted: Thu Feb 14, 2013 4:51 pm Post subject: 129 |
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| extropalopakettle wrote: |
| (I carefully avoided attempting to divide the number 1-0.999... by anything to obtain X, as then it would use its superpowers to transform into an infinite string to protect itself from division) |
| Quote: |
| I'm picturing some xkcd style comic where 0.999... transforms back and forth between number and infinite string whenever threatened by mathematical operations. |
Oh my goodness, these two lines caused me so much laughter. I'm still laughing as I type this. (I may be a bit stressed with school.)
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esme*
Guest
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| Posted: Fri Feb 15, 2013 9:24 am Post subject: 130 |
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| bgg1996 wrote: |
| extro...* wrote: |
| Death Mage wrote: |
| Alright, in .999... - .999... how many times do you have to subtract 9 from 9? |
You only need to do it once, see the answer is 0, and know it will be 0 for ALL OF THEM. |
Oh cool, really?
I'm gonna use this awesome new proof method you just informed me of.
| Code: |
X = 1+2+4+8+16+32+64+128+...
2X = 2+4+8+16+32+64+128+...
2X - X = 2+4+8+16+32+64+128+... - (1+2+4+8+16+32+64+128+...)
0+2+4+8+16+32+64+128+...
- 1+2+4+8+16+32+64+128+...
= -1+0+0+0+0+0+0+0+0+0+...
X = -1+0+0+0+0+0+0+0+0+0+...
X = -1 |
I always secretly knew I could apply basic algebra to infinite series to get an answer that doesn't make much sense. |
Ok, my self-control is wavering, so let me add to the conversation that the above is a valid equation in the 2-adics, since -1 is simply the unique Banach limit of this series.
Also, it is perfectly useful and meaningful to calculate with diverging series to get correct results for ordinary numbers in the end.
Since Euler, mathematicians have formalized these ideas, so phycisists had to pick up the slack on illegal calculations that give correct results. |
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