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 Yet another discussion about 0.99... Goto page Previous  1, 2, 3, 4
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Posted: Thu Feb 14, 2013 3:34 am    Post subject: 121

 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.
LordKinbote
Daedalian Member

Posted: Thu Feb 14, 2013 4:07 am    Post subject: 122

 jadesmar wrote: Obviously the bit that claims 1/3=0.333... Is just an approximation.

And it's off by...how much, exactly?
MNOWAX
0.999... of a Troll

Posted: Thu Feb 14, 2013 4:49 am    Post subject: 123

 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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MNOWAX
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June 21st, 2004 Member

Posted: Thu Feb 14, 2013 5:01 am    Post subject: 124

 MNOWAX wrote: Do the long division.

Understatement of History.
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extropalopakettle
No offense, but....

Posted: Thu Feb 14, 2013 9:34 am    Post subject: 125

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").
extropalopakettle
No offense, but....

 Posted: Thu Feb 14, 2013 9:46 am    Post subject: 126 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)
LordKinbote
Daedalian Member

Posted: Thu Feb 14, 2013 12:59 pm    Post subject: 127

 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?"
extropalopakettle
No offense, but....

 Posted: Thu Feb 14, 2013 1:11 pm    Post subject: 128 I'm picturing some xkcd style comic where 0.999... transforms back and forth between number and infinite string whenever threatened by mathematical operations.
Jedo the Jedi
Paragon in Training

Posted: Thu Feb 14, 2013 4:51 pm    Post subject: 129

 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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Posted: Fri Feb 15, 2013 9:24 am    Post subject: 130

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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