I just broke math...

Quote:

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Originally Posted by 'spudstar99',index.php?page=Thread&postID=201848#p ost201848

easy 9* (1/9) = 1 not 0.9(repeating)
and 9*0.1(repeating) = 0.9(repeating)
they are not equal
just as info

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The repeating part is what makes them equal. Let us try this one again. If 1/9 is .1(repeating), then 9 * (1/9) is .9(repeating). But 9 * (1/9) is 1. If 9 * (1/9) is equal to 9 * (1/9), which it is, then .9(repeating) is equal to 1.

I'll say it again - the REPEATING is what makes them equal. Well, okay. I lied. The repeating is helping me here. What really makes them equal is the transitive property of equality. In English, all I'm saying is that if a=b and a=c, then b=c by definition. Here, a = 9 * (1/9), b = .9(repeating), and c = 1.

.9(repeating) = 1

Question?

EDITED: While correct, the above argument is assuming. Many people aren't going to notice that 1/9 and .1(repeating) can stand in for each other. Because of this, I've assumed a recursive application of the transitive property of equality. I'm going to provide an even more basic argument to clarify.

1/9 = .111(repeating)
Multiply both sides of the equation by 9. (To avoid the assumption of clarity made by my last argument)
9 * (1/9) = 9 * .111(repeating)
The previous line yields this: 1 = .999 (repeating)

Is that more helpful?

Quote:

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Originally Posted by 'Frosty',index.php?page=Thread&postID=201877#post2 01877

Why do I feel the need to beat you all up??? :P

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Because we probably deserve it.

ok thats the problem ...
because (1/9) is .1(repeating )
but 0.1(repeating)*9 = 1
proof this with your calc ...
sincery spud
ps we all suck

[quote='spudstar99',index.php?page=Thread&postID=20 1940#post201940]but 0.1(repeating)*9 = 1[/quote]
To expand that, 0.1(repeating) * 9 = .9(repeating) = 1
This is the same implied equality that you missed out of my last post (i.e. that .9(repeating) can stand in for 9 * (1/9)).

They're equal. [url='http://en.wikipedia.org/wiki/0.999...']Here[/url] are a few other proofs if you're interested.

EDIT: Also, you can't use a calculator as proof of anything. There were many times when a calculator gave me a result of 1.8x10^-18 when it meant zero. While I was in college, a coworker claimed that PI was not irrational because he used one of the IT Labs computers at the University to find the EXACT value. The computer is going to make an educated guess. No computer can do math on an infinite number of decimal places and thus using one in an argument about infinite decimal places is guaranteed to give a wrong result.

It's hard to break real math using imaginary numbers. The value of .9(repeating) can't even be displayed, let alone fully comprehended, it is used to give a visual respentation of a value, but isn't the actual value itself. The real value of 1 divided by 9 is 1/9, not .1(repeating). Theoretically the same thing, but at some point all calculations attempting to use the repeating value has to crop the value off otherwise it goes on forever, which means that you are already using rough estimates not precision.

Stick to the fractions, as they don't lie. Repeating decimal values would kick your cat if they could.

.9(repeating) had better = 1, or all those calculus classes I took were pointless... not to mention the diff eqs class.

In theory, yes. On a piece of paper or calculator, no.

Said another way, the person has to be told that .9(repeating) = 1, since writing the math formulas out by hand or trying to work it on a calculator turn up invalid results. If you're trying to actually work on a math problem using these values, you're less likely to hurt your brain matter if you stick with the fractions (assuming there is one to represent the value).

Personal note, I never want to deal with calculus ever ever again.

Quote:

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Originally Posted by 'Taliesin',index.php?page=Thread&postID=201989#pos t201989

... the person has to be told that .9(repeating) = 1, since writing the math formulas out by hand or trying to work it on a calculator turn up invalid results.

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Proof to the contrary was provided already.

1/9 = .111(repeating)
9 * (1/9) = 9 * .111(repeating)
1 = .999(repeating)

It works on paper. As per the (well-documented) Wikipedia article I linked, the trick here is to remember the repeating value. There is NOT a final nine in that sequence of decimal places. A calculator or a computer cannot be used to provide mathematical theory since it is ONLY an emulator of the theory, not the verification method.

Quote:

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Originally Posted by 'Taliesin',index.php?page=Thread&postID=201974#pos t201974

The value of .9(repeating) can't even be displayed, let alone fully comprehended...

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It is the value of 1. .999(repeating) is a real number. It has a real value. That value is one. I comprehend it just fine.

Quote:

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Originally Posted by 'Basilikos',index.php?page=Thread&postID=202019#po st202019

Proof to the contrary was provided already.

1/9 = .111(repeating)
9 * (1/9) = 9 * .111(repeating)
1 = .999(repeating)

It works on paper. As per the (well-documented) Wikipedia article I linked, the trick here is to remember the repeating value. There is NOT a final nine in that sequence of decimal places. A calculator or a computer cannot be used to provide mathematical theory since it is ONLY an emulator of the theory, not the verification method.

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The same article also provides proofs where the logic breaks. It depends on the number system you use. Otherwise you could end up with negative and positive values of zero, where zero is supposed to be neither positive nor negative.

One example is blackholes. The theory is sound, yet it breaks when you apply it to real world applications that require it to be true. They still can't get blackhole theory to work with infinitesmals, so they just say that the rules of phsyics "seem to disappear". It could just turn out that they are using bad formulas, or that blackholes require all new formulas.

Don't get me wrong, not trying to start a flame war, but if you dig deep into a lot of the theory, at the very least you learn that the proof isn't true in all cases. Doesn't necessarily make it wrong, but leaves it more in the realm of accepted theory than hard fact.