Get off your Ath let's do some Math!

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|3lack|ce
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Get off your Ath let's do some Math!

Post: # 125079Post |3lack|ce
Wed Jan 14, 2009 8:20 pm

Ok, so here's the one that'll really bake your noggin...

1/3 can be expressed as .333~

2/3 can be expressed as .666~

1/3 + 2/3 = 1

.333~ + .666~ = .999~

Ergo .999~ = 1.

Wtf? No matter how far down the line you go in .99999999999~ it will never, EVER reach one, but here is conclusive proof it does. Someone splain it to me before my head explodes? No fair quoting Cecil Adams, I've already read his archived column on this and I'm still obfuscated.


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Re: Get off your Ath let's do some Math!

Post: # 125080Post cgkanchi
Wed Jan 14, 2009 9:04 pm

At one point during the series of 0.99999999999999's, the number gets so close to 1 that it might as well be. Where that point is, is up to you to decide. Alternatively, you can say that there is no perfect way to represent the fraction 1/3 in decimals, but that's the best we can do :)

0.9 != 1
0.99 !=1
0.999 != 1
0.9999999999999 ~= 1 (approximately equal).

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Re: Get off your Ath let's do some Math!

Post: # 125082Post Vorlin
Wed Jan 14, 2009 9:25 pm

This is along the lines of pi and what it represents. Pi is simply 22/7 and is 3.141529~ and it will never end. 1/3 = .333~ forever, same for 2/3 = .666~ forever and no matter how many places after the decimal point you go, 1/3 + 2/3, while equaling 1 in our world, will never be 1...but it will be .9999999999999999999999999999999999999999999999999~ which, in our terms, is 1.
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Re: Get off your Ath let's do some Math!

Post: # 125086Post Egaladeist
Wed Jan 14, 2009 9:31 pm

If I go to the Market and buy something worth one dollar...but it's on sale for ( 1/3rd ) 33% off...and I ask for exact change...shouldn't I get 66.6666666666666666666666- cents back?

Hey...it adds up :rolf6:

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Re: Get off your Ath let's do some Math!

Post: # 125093Post imnogeek
Thu Jan 15, 2009 10:49 am

Sort of inline with another thread here... should the USA go decimal, well it does make it easier (see above) :mrgreen:
How did you come to that conclusion?

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Re: Get off your Ath let's do some Math!

Post: # 125097Post |3lack|ce
Thu Jan 15, 2009 3:07 pm

At one point during the series of 0.99999999999999's, the number gets so close to 1 that it might as well be.
Ah, but there's the rub!

.99999999~ NEVER ENDS - so you cannot stop the 9's from coming. You might WANT to stop them, but they keep coming, and they get infinitely closer, but always *just* miss 1, kinda like taking a piece of paper and cutting it in half until you have nothing left. You might get down to pieces smaller than individual electrons, but speaking mathematically, you will NEVER run out of paper.

You're all correct though - it's due to the imperfection of fraction to decimal expressions, a basic flaw in math, much like trying to express the square root of negative 1 before imaginary numbers were invented.

I need a .999999999999999999999999~ hug.
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Re: Get off your Ath let's do some Math!

Post: # 125102Post Aspman
Thu Jan 15, 2009 4:05 pm

It's an abstraction. Eventually after several hundred miles of 9s there is a banana :mad:
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Re: Get off your Ath let's do some Math!

Post: # 125105Post |3lack|ce
Thu Jan 15, 2009 4:49 pm

Nope, that's just a banana peel - placed carefully so as to trip up unwary mathematicians.
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Re: Get off your Ath let's do some Math!

Post: # 125130Post SirDice
Fri Jan 16, 2009 1:12 am

Try and solve y=1/x for x=0 :P

Man, that's a long time ago.. Even had to look it up..
I think you can solve this problem with a mathematical limit. If you take n to infinity..

http://en.wikipedia.org/wiki/Limit_of_a_sequence
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Re: Get off your Ath let's do some Math!

Post: # 125135Post cgkanchi
Fri Jan 16, 2009 1:50 am

AFAIK, you can't solve y=1/x where x=0. However, you can solve lim(x->0)1/x which is equal to infinity. :)
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Re: Get off your Ath let's do some Math!

Post: # 125136Post SirDice
Fri Jan 16, 2009 1:51 am

cgkanchi wrote:AFAIK, you can't solve y=1/x where x=0. However, you can solve lim(x->0)1/x which is equal to infinity. :)
Exactly :D

n to infinity for the number of 6's or 3's in 0.6666~ and 0.3333~ and the answer will be 1 :mrgreen:
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Re: Get off your Ath let's do some Math!

Post: # 125138Post |3lack|ce
Fri Jan 16, 2009 2:12 am

Within the normal rules of mathematics, x can never equal zero in that equation, because you can never divide by zero.

y = 1/x is infinity. y can always equal 1 divided by any number not zero, but ya can't divide by zero.

Ever plotted y=1/x on a graph?

Try y = x^2 + 2(x) + 1 sometime :)
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Re: Get off your Ath let's do some Math!

Post: # 125149Post SirDice
Fri Jan 16, 2009 12:19 pm

|3lack|ce wrote:Within the normal rules of mathematics, x can never equal zero in that equation, because you can never divide by zero.

y = 1/x is infinity. y can always equal 1 divided by any number not zero, but ya can't divide by zero.

Ever plotted y=1/x on a graph?
Yes, with limits you can :mrgreen:
Another nice variation on the infinity theme... lim(x->infinity)1/x = 0
Try y = x^2 + 2(x) + 1 sometime :)
Nice parabola :)

I can probably solve it too ;)
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Re: Get off your Ath let's do some Math!

Post: # 125161Post Ally
Fri Jan 16, 2009 11:31 pm

My eyes have glazed over :mad:
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Re: Get off your Ath let's do some Math!

Post: # 125177Post Kwiep
Sat Jan 17, 2009 8:57 pm

I've had an argument about that before, it usually ends in a load of crap. It depends on certain math definitions you use. There's other things like this, for example:
http://en.wikipedia.org/wiki/Two_envelopes_problem
And I think there was an article on the xkcd blag once:
http://blag.xkcd.com/2008/09/09/the-god ... treadmill/
The airplane/treadmill problem is similar. It contains a basic ambiguity, and people resolve it one of a couple different ways. The tricky thing is, each group thinks the other is making a very simple physics mistake. So you get two groups each condescendingly explaining basic physics and math to the other. This is why, for example, the airplane/treadmill problem is a banned topic on the xkcd forums (along with argument about whether 0.999… = 1).
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