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Offlineamyloid
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Registered: 03/08/03
Posts: 980
Last seen: 2 years, 10 months
mind bender...
    #1362589 - 03/10/03 10:26 AM (13 years, 8 months ago)

.99(bar) is = to 1:

1/3 = .33(bar) correct?(lets call this statement 1)
3*1/3 = 1 correct?(2)
3*.33(bar) = .99(bar) correct?(3)
.99(bar) = 1

any 2 differnt numbers has a number between it, .99(bar) and 1 has nothing between it

can a mathmatician prove this wrong...please, ive done broke myself =(

-doc


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"A human being is part of a whole, called by us the Universe, a part limited in time and space. He experiences himself, his thoughts and feelings, as something separated from the rest--a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest us. Our task must be to free ourselves from this prison by widening our circles of compassion to embrace all living creatures and the whole of nature in its beauty."
-Al Einstein


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Invisibleluvdemshrooms
Two inch dick..but it spins!?


Registered: 11/29/01
Posts: 33,791
Loc: Lost In Space
Re: mind bender... [Re: amyloid]
    #1362635 - 03/10/03 10:44 AM (13 years, 8 months ago)

EDIT: Been out of school way too long.


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You cannot legislate the poor into prosperity by legislating the wealthy out of prosperity. What one person receives without working for another person must work for without receiving. The government cannot give to anybody anything that the government does not first take from somebody else. When half of the people get the idea that they do not have to work because the other half is going to take care of them and when the other half gets the idea that it does no good to work because somebody else is going to get what they work for that my dear friend is the beginning of the end of any nation. You cannot multiply wealth by dividing it. ~ Adrian Rogers


Edited by luvdemshrooms (03/10/03 03:00 PM)


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Offlineamyloid
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Registered: 03/08/03
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Re: mind bender... [Re: luvdemshrooms]
    #1362731 - 03/10/03 11:27 AM (13 years, 8 months ago)

.99(bar) means .9999999999999999999999(with 9's continuing towards infinity)


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"A human being is part of a whole, called by us the Universe, a part limited in time and space. He experiences himself, his thoughts and feelings, as something separated from the rest--a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest us. Our task must be to free ourselves from this prison by widening our circles of compassion to embrace all living creatures and the whole of nature in its beauty."
-Al Einstein


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OfflineToxicManM
Bite me, it's fun!
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Re: mind bender... [Re: amyloid]
    #1362803 - 03/10/03 11:56 AM (13 years, 8 months ago)

You are correct. Here is a simple algebraic proof.

0.9999... = x
9.9999... = 10x Multiply by 10
9 = 9x Subtract first statement from second
1 = x Divide both sides by 9

There are no numbers between them because they are the same number. Any two different real numbers have an infinite number of real numbers between them.


--------------------
Happy mushrooming!


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OfflineSeussA
Error: divide byzero

Folding@home Statistics
Registered: 04/27/01
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Re: mind bender... [Re: amyloid]
    #1362808 - 03/10/03 11:58 AM (13 years, 8 months ago)

Quote:

.99(bar) is = to 1:




This is not correct.

.99(bar) = .99(bar), not 1.00(bar)

You could also say that .99(bar) = 1 - 1/inf (might have to take the limit, been a while since calc)





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OfflineAnnoA
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Re: mind bender... [Re: Seuss]
    #1362875 - 03/10/03 12:30 PM (13 years, 8 months ago)

>This is not correct.

But ToxicMan just gave you a mathematical proof that 0.99(bar) = 1 .


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InvisibleTheHateCamel
Research &Development -DBK
Registered: 01/31/03
Posts: 15,738
Re: mind bender... [Re: amyloid]
    #1363020 - 03/10/03 01:32 PM (13 years, 8 months ago)

.


Edited by TheHateCamel (12/05/07 10:58 PM)


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OfflineToxicManM
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Re: mind bender... [Re: TheHateCamel]
    #1363847 - 03/10/03 07:01 PM (13 years, 8 months ago)

The (bar) part is trying to convey the mathematical notation used to indicate an infinitely repeating decimal. So he's referring to the number 0.99999999999999 (with an infinite number of 9's).


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Happy mushrooming!


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Anonymous

Re: mind bender... [Re: ToxicMan]
    #1363941 - 03/10/03 07:37 PM (13 years, 8 months ago)

Quote:

0.9999... = x
9.9999... = 10x Multiply by 10
9 = 9x Subtract first statement from second
1 = x Divide both sides by 9




Here we run into the same problem. To prove that 0.9(bar) equals 1, you assume that 0.9(bar) does equal 1 in the third step. However, 0.9(bar) times 9 is really equal to 8.9(bar).

0.9(bar) does not equal 1. Merely the limit as the number of decimal places approaches infinity of 0.9(bar) is equal to 1. Simply put, 0.9(bar) approaches 1, but never equals it.


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OfflineToxicManM
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Re: mind bender... [Re: Anonymous]
    #1363996 - 03/10/03 08:00 PM (13 years, 8 months ago)

No. I used the 3 dots to indicate an infinite repetition of the 9's, instead of the (bar). If I multiply 0.9999 (infinite number of 9's) by 10 I get 9.9999 (infinite number of 9's). I can subtract the different sides of the equation from each other because they are equal expressions. And the difference will be exactly 9. Since 9x = 9, x must be equal to 1.

This proof is based on the method for converting a repeating decimal to a fraction. In this case it demonstrates that the denominator of the fraction is 1.


--------------------
Happy mushrooming!


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Anonymous

Re: mind bender... [Re: ToxicMan]
    #1364031 - 03/10/03 08:15 PM (13 years, 8 months ago)

OK, I wrote it out and it works, algebrically.  However, because infinity can never be reached, would it not also be true that 1 is merely the limit?

It is very interesting how a process learned in middle school can solve such a problem... I'm going to take this one to my calculus teacher, see what he thinks.

PS: Problems like this kick ass :laugh:


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InvisibleinfidelGOD
illusion

Registered: 04/18/02
Posts: 3,040
Loc: there
Re: mind bender... [Re: ToxicMan]
    #1364270 - 03/10/03 11:36 PM (13 years, 8 months ago)


0.9999... = x
9.9999... = 10x Multiply by 10
9 = 9x Subtract first statement from second
1 = x Divide both sides by 9


the algebra is correct but something still bothers me...

check it out:

if .9(bar) = 1

then

(1/inf) = 0 ?

since they both represent limits?
:confused:

 


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OfflineToxicManM
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Re: mind bender... [Re: infidelGOD]
    #1364693 - 03/11/03 05:13 AM (13 years, 8 months ago)

stonedfish - yes, that's another way of thinking of it. You're making the statement into the sum as x=1 to infinity of 9 times 10^-x, where the limit indeed approaches 1. By using the (bar) notation we are indicating the actual existence of an infinite number of digits, so 0.9999(bar) becomes actually another way to write the number 1. Obviously, a less convenient way.

infidelGOD - yes, 1/infinity = 0. In fact, for all real numbers x > 0, x/infinity = 0.


If you guys are developing an interest in infinity I can recommend Infinity and the Mind - The Science and Philosophy of the Infinite by Rudy Rucker. His PhD thesis was on Transfinite Numbers, so he knows about about infinities. Here's a link to his home page. He teaches mathematics at San Jose State University in California and writes some interesting science fiction.


--------------------
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InvisibleinfidelGOD
illusion

Registered: 04/18/02
Posts: 3,040
Loc: there
Re: mind bender... [Re: ToxicMan]
    #1364702 - 03/11/03 05:17 AM (13 years, 8 months ago)

hhmmmmm....

shouldn't it be:
for all real numbers x >= 0, x/infinity = 0 since 0/x is always 0?

so 1/inf = 0/inf?

OK my mind is bent  :confused:




 


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OfflineToxicManM
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Re: mind bender... [Re: infidelGOD]
    #1365166 - 03/11/03 08:28 AM (13 years, 8 months ago)

Yeah, zero/infinity should be zero, too.

You have to be real cautious about including zeros and infinities in the same expression. A lot of those expressions are undefined - there is no meaningful result. A typical example is zero * infinity. Typically the ones that give results are arrived at through limits. Remember that you have to investigate the limits from both above and below.


--------------------
Happy mushrooming!


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Anonymous

Re: mind bender... [Re: ToxicMan]
    #1365596 - 03/11/03 10:51 AM (13 years, 8 months ago)

On that note, how can infinity^infinity still equal infinity?


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OfflineToxicManM
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Re: mind bender... [Re: Anonymous]
    #1366031 - 03/11/03 01:11 PM (13 years, 8 months ago)

Actually, it depends on which definition of infinity is being used. In Rudy Rucker's book there's an entire section on Transfinite Numbers (what a surprise, since his thesis was on them). The various transfinite numbers are derived in various ways from set theory, and you get an entire system of numbers which are all infinite but of different relative magnitudes. It's fairly complicated, and a lot more than I could explain without just copying a lot of pages.

If you really have an interest to that level in infinity, I strongly recommend you find a copy of his book and read it. There's a lot more to the topic that you'd suspect at first.


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Happy mushrooming!


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InvisibleTeragon
Noddy

Registered: 02/21/01
Posts: 36,253
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Re: mind bender... [Re: Anonymous]
    #1366294 - 03/11/03 02:50 PM (13 years, 8 months ago)

In my Calc class, infinity*infinity is considered indeterminate. This is when considering limits and trying to evaluate/differentiate them. We use a method to get around indeterminate forms of limits, called l'Hospitale's. Not sure how applicable this info is in this situation, but I'm pretty sure inifinity*inifinity cannot be evaluated directly, much like ToxicMan was talking about. :grin: 


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