Why America Is Falling Behind In Math

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altima_boy_2001
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RE: Why America Is Falling Behind In Math 2009/03/31 02:56:08 (permalink)
It's a sneaky trick

I don't understand why people keep implying there is some trick to this. It is a proof that starts with definitions and function and applies valid, logical manipulation to show something that on the surface appears absurd or contradictory. If you cannot find fault within the argument then you cannot deny the result. It is strange result indeed, but any logical system will contain unintended, contradictory, or unexplainable results no matter how well designed.



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Texrat
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RE: Why America Is Falling Behind In Math 2009/03/31 03:01:27 (permalink)
I still say it demonstrates our inability to comprehend what's really going on. Just like we can't explain the freaky aspects of quantum mechanics.

There's just no way an infinitely repeating sequence of .999... can be exactly the same as the discrete number 1.

Try other math tricks and you'll see. For instance, divide 1 by 2. Now divide .999... by 2. Oops.
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Roflcopter
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RE: Why America Is Falling Behind In Math 2009/03/31 08:52:24 (permalink)

I don't understand why people keep implying there is some trick to this. It is a proof that starts with definitions and function and applies valid, logical manipulation to show something that on the surface appears absurd or contradictory. If you cannot find fault within the argument then you cannot deny the result. It is strange result indeed, but any logical system will contain unintended, contradictory, or unexplainable results no matter how well designed.


I hope you're not seriously calling this a proof of any sorts. It's just sleight of hand. Moving the dot or comma left or right is not an operation that alters any intrinsic value (other than scaling it up or down decimally).

There is no invisible rounding function. Multiplying by ten (for no reason) and then removing it again, does nothing with the infinity, only the integers involved.
post edited by Roflcopter - 2009/03/31 08:54:25

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#63
Texrat
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RE: Why America Is Falling Behind In Math 2009/03/31 10:35:22 (permalink)
What he said.
#64
Bristol_Jonesey
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RE: Why America Is Falling Behind In Math 2009/03/31 12:02:51 (permalink)

ORIGINAL: jhughs

You start off with x=0.999..., then multiply by 10, then subtract the first row from the second row, then divide by 9:

x = 0.999...
10x = 9.999...
10x - x = 9.999... minus 0.999...
9x = 9
x = 1
therefore x = 0.999... = 1

which proves that I was a rock guitarist who led a secret life as a geeky math/comp sci major.



Yeah, but the error is easy to spot:


10x <> 9.999

10x = 9.990

10x -x = 9.990 -.999 = 8.991
9x = 8.991
x = .999


Take that Euclid!!!!

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Roflcopter
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RE: Why America Is Falling Behind In Math 2009/03/31 12:05:09 (permalink)
Erm, the dots ... behind the row of nines means they continue endlessly. So there is no 9990, ever. It's shorthand, sometimes they print a slash thru the last digit to show it continues endlessly, as well.

The error is in switching integers without need, nothing happens on the 'right hand side'.

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Jonbouy
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RE: Why America Is Falling Behind In Math 2009/03/31 12:45:09 (permalink)
I like 1 / 7 that makes such a pretty pattern.

I mean if yer gonna recur forever do it in sequence I say, and still return to the whole if required.

Now theres the secret of eternal life, right there. Never mind yer 42 although that of course is also divisble by 7 and likely contains some merit.
post edited by Jonbouy - 2009/03/31 12:57:40

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#67
Beagle
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RE: Why America Is Falling Behind In Math 2009/03/31 13:27:53 (permalink)
sorry, but anyone who's had Calculus I should know that 0.999... does not = 1. the "..." means that the number repeats to infinity - you cannot equate an infinitely repeating fraction with an integer - they're not the same number. It's a LIMIT equation only and means that lim x-->1 f(x) = 1 but that is NOT the same thing as x = 1.

http://www.analyzemath.com/calculus/limits/introduction.html
http://en.wikipedia.org/wiki/Limit_(mathematics)

the "proof" above is not applicable - just like Rob (roflcopter) is saying. you're comparing apples and oranges.

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space_cowboy
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RE: Why America Is Falling Behind In Math 2009/03/31 13:30:49 (permalink)
Or the limit x-->0 of 1-x =1. But that is the limit as x approaches (BUT DOES NOT QUITE EVER GET TO) 0.

But for any x infinitesimally greater than zero f(x) would be 0.9999999999999999 whatever
post edited by space_cowboy - 2009/03/31 13:51:23

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Roflcopter
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RE: Why America Is Falling Behind In Math 2009/03/31 13:41:46 (permalink)
Logical steps seen from a distance can be as deceiving as a computer program - it all looks legit, until you try to run it, and it crashes hopelessly.

Rationality and logic are not the same thing. Logic is bound by the limits of the experiment. Steps can look OK, but still be in thin air, or a vacuum, more like. You should never forget the big picture. Like the Logician who bought 27 cauliflowers because they were so cheap, but had no fridge to store them. Logic says buy, rationality says get real.

Reverse is also true. Sometimes calculations seem improbable, but they are absolutely correct, only the outcome goes against every intuition. I should have a doozy somewhere, see if I can dig that up.

I'm a perfectionist, and perfect is a skinned knee.
#70
Texrat
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RE: Why America Is Falling Behind In Math 2009/03/31 14:42:08 (permalink)
Hee hee hee... [imagine devil smiley here]
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Guitarmech111
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RE: Why America Is Falling Behind In Math 2009/03/31 16:23:56 (permalink)

ORIGINAL: mike_mccue

so what am I missing?

3² + 4² = 5²

are you guys using that fancy trigonometry and just afraid to round out?



Constructtion workers use that formula.

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space_cowboy
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RE: Why America Is Falling Behind In Math 2009/03/31 18:00:52 (permalink)
Hey Con Man
PM me. I want to know when you have any events. Plus I am always looking for people to record with. My AIM changed.

Some people call me Maurice
 
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jhughs
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RE: Why America Is Falling Behind In Math 2009/04/01 21:53:29 (permalink)
Dang it, I told myself not to look at this thread again, but I did anyway.

There was some confusion about the proof: it wasn't just moving the decimal point, the "trick" was to multiply the first equation by 10, then subtract the first equation from the new one to get 9x = 9.

Yes, 0.999... = 1, no tricks.
0.999... divided by 2 = 0.4999... = 0.5

Apparently the thing we all struggle with is what it means to be infinitely close to something without reaching it.

I didn't appreciate that this would result in such controversy, but there's an okay write-up on Wikipedia: http://en.wikipedia.org/wiki/.999...

Or maybe the mathematicians are wrong and there's some special corner of hell for misguided mathematicians that is infinitely close to heaven without converging into heaven.

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Roflcopter
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RE: Why America Is Falling Behind In Math 2009/04/02 05:59:54 (permalink)
it wasn't just moving the decimal point, the "trick" was to multiply the first equation by 10, then subtract the first equation from the new one to get 9x = 9.


Quote:

Multiplying by ten (for no reason) and then removing it again, does nothing with the infinity, only the integers involved.

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#75
Texrat
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RE: Why America Is Falling Behind In Math 2009/04/02 09:06:10 (permalink)
Also, one has to round up .499... to get that nice discrete 5 integer. It doesn't come cleanly from 0.999... / 2.

This really is a sort of parlor trick but there are professional mathematicians who will religiously defend it. The value of what you're saying, Rofl, seems to be lost on some.
#76
Jessie Sammler
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RE: Why America Is Falling Behind In Math 2009/04/02 20:00:27 (permalink)
Apparently the thing we all struggle with is what it means to be infinitely close to something without reaching it.


Boy, you can say that again.
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jhughs
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RE: Why America Is Falling Behind In Math 2009/04/02 21:23:38 (permalink)
Well, I never thought I find myself defending a mathematical concept, but I’ll give it one last shot.

Try thinking of it from the other way around. Ask yourself “How could 0.999… be anything but 1?”

It’d go something like this:
1) If 0.999… is less than one, then there must be a number between 0.999… and 1.
2) But if there’s a number between 0.999…. and 1, then we haven’t run the 9s out to infinity.
3) Therefore, since there can be no number between 0.999… and 1 then 0.999… can’t be less than 1 so they must be equivalent.

Anyway, I’m done and we can all be glad that few of us will ever need to worry about infinity… unless this discussion continues… then maybe it can’t come soon enough.




Apparently the thing we all struggle with is what it means to be infinitely close to something without reaching it.



Boy, you can say that again.


Oh yeah, right, isn't there a Tom Petty lyric that says that?


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Texrat
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RE: Why America Is Falling Behind In Math 2009/04/02 21:25:27 (permalink)
I'll grant ya equivalent but not equal. Call it a compromise.
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Roflcopter
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RE: Why America Is Falling Behind In Math 2009/04/02 21:30:52 (permalink)
1) If 0.999… is less than one, then there must be a number between 0.999… and 1.
2) But if there’s a number between 0.999…. and 1, then we haven’t run the 9s out to infinity.
3) Therefore, since there can be no number between 0.999… and 1 then 0.999… can’t be less than 1 so they must be equivalent.


OK - but that's Zeno's paradox of Achilles and the tortoise, revisited.

http://en.wikipedia.org/wiki/Zeno%27s_paradoxes

And we all know who wins that caper.

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jhughs
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RE: Why America Is Falling Behind In Math 2009/04/02 23:09:54 (permalink)

ORIGINAL: Roflcopter


OK - but that's Zeno's paradox of Achilles and the tortoise, revisited.

http://en.wikipedia.org/wiki/Zeno%27s_paradoxes

And we all know who wins that caper.


Good one, and I confess I wasn't familiar with it. (My mother was the philosophy major but didn't get to stay among us long enough to pass her knowledge on to me.)

For a second there I thought you were going to say "Tortoises. It's tortoises all the way down."

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Roflcopter
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RE: Why America Is Falling Behind In Math 2009/04/03 04:13:20 (permalink)
Tortoises. It's tortoises all the way down.


Mr. Pratchett has been remarkably astute in many of his quips

http://www.newscientist.com/article/mg20127011.600-can-fractals-make-sense-of-the-quantum-world.html?full=true

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Jonbouy
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RE: Why America Is Falling Behind In Math 2009/04/03 08:59:46 (permalink)

ORIGINAL: Jessie Sammler

Apparently the thing we all struggle with is what it means to be infinitely close to something without reaching it.


Boy, you can say that again.


Man, when that avatar speaks it really says something.

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In the meantime we should all go shopping to console ourselves" - Banksy
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Jessie Sammler
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RE: Why America Is Falling Behind In Math 2009/04/04 19:54:50 (permalink)
Good thing it's the avatar speaking and not me.

Bottom line, it's so easy to grow to maturity here in the States being a completely ignorant twat, regardless of your background or education. I, for one, revel in it.
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space_cowboy
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RE: Why America Is Falling Behind In Math 2009/04/05 11:37:03 (permalink)

ORIGINAL: Jonbouy

I like 1 / 7 that makes such a pretty pattern.

I mean if yer gonna recur forever do it in sequence I say, and still return to the whole if required.

Now theres the secret of eternal life, right there. Never mind yer 42 although that of course is also divisble by 7 and likely contains some merit.



Jobouy
If you like 1/7 (0.142857....)
Try this trick
Take 999,999 and divide by 7. 142857. Store that in your calculator. To keep me from typing it over and over again, I am going to call it X.
Multiply X times 2. 285714. Same digits, same order, but rotated around a bit.
Multiply X times 3. 428571. Same digits, same order, but rotated around a bit.
Times 4
Times 5
Times 6
All have the same phenomenon.


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Roflcopter
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RE: Why America Is Falling Behind In Math 2009/04/05 11:41:12 (permalink)
Here's a nice one to check your calculator, in case of doubt:

12345679 (no 8) times 9, times 18, times 27 etc you get the pattern.

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#86
space_cowboy
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RE: Why America Is Falling Behind In Math 2009/04/05 11:46:09 (permalink)

ORIGINAL: Roflcopter

Here's a nice one to check your calculator, in case of doubt:

12345679 (no 8) times 9, times 18, times 27 etc you get the pattern.

Another old favorite of mine.
Or 1/1.0125 (need some digits here to see the effect).
Or 1/98 )less obvious - but you should get the powers of 2 (01 02 04 08 16 32 then the three digits start to add on top of each other but it still works). Try successive multiplies by 100 and subtract the power of 2.


Some people call me Maurice
 
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Roflcopter
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RE: Why America Is Falling Behind In Math 2009/04/05 12:53:27 (permalink)
You ever played with google calculator? Try typing 'once in a blue moon' in google, this will start an easter egg in the calculator.

same with 'number of horns on a unicorn'

and ofcourse:

answer to life the universe and everything


I'm a perfectionist, and perfect is a skinned knee.
#88
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