I just broke math...

[bluntman]

O.K.... was doing some doodling and figured I'd crunch some numbers just for the hell of it :P what can i say i'm bored :)
well while i was messing around i discovered something..
lets say you are dealing with the number .9(repeating) ..
set N=.9(repeating)
if N=.9(repeating) then 10N=9.9(repeating)
10N-N=9.9(repeating)-.9(repeating)=9=9N
take 9N=9 and separate the N
9N/9=1
N=1
so... N=1 but N also = .9(repeating)

now i know that .9 repeating approaches 1 as it approaches the infinity position, but it never reaches 1...

alternatively..
lets take .1(repeating)
.1(repeating)=1/9
.2(repeating=2/9
.3(repeating=3/9
continue this pattern and you'll see were I'm going...
.9(repeating)=9/9??

either I'm extremely tired or I've successfully broken math :P someone let me know which one it is lol

[Gomotron]

O.K.... was doing some doodling and figured I'd crunch some numbers just for the hell of it :P what can i say i'm bored :)
well while i was messing around i discovered something..
lets say you are dealing with the number .9(repeating) ..
set N=.9(repeating)
if N=.9(repeating) then 10N=9.9(repeating)
10N-N=9.9(repeating)-.9(repeating)=9=9N
take 9N=9 and separate the N
9N/9=1
N=1
so... N=1 but N also = .9(repeating)

now i know that .9 repeating approaches 1 as it approaches the infinity position, but it never reaches 1...
Your problem occurs when, to me, you seem to arbitrarily say 9=9N.

I'm not sure where you're coming up with that.


As far as your other observation:
I think that the basic equality is flawed. I do not think that .1111--- is equivalent to 1/9, although on the surface it would appear to be the case.

[bluntman]

well. with this i am stating that when you take 10N and subtract N from it you get 9 so 9N=9 and so far as the 1/9=.1 repeating its true but as for if it remains true in higher mathematics I'm unsure... like for the purposes of calc1-2 0/0 is undefined and not an acceptable answer whereas when you reach calc3-4 / dif. eq. 0/0 can be infinity or 1 ect...

anyhow I'm going to take this as a i need to sleep more and do this less :P
I'll mention it to my professor tomorrow and see if she gets a kick out of it heh

[thinus]

well. with this i am stating that when you take 10N and subtract N from it you get 9

No you don't, you get 9N.

[Basilikos]

Sorry, but we've all seen this one before.

And yes, it's true.


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

Questions?

And while I'm here, why is it that everyone who posts this on any given forum (and I've seen it on many) has to make it so damn complicated? Why not used the four lines I've posted above? It is just for the sake of making someone's head spin?

[Basilikos]

I'll mention it to my professor tomorrow and see if she gets a kick out of it heh

She won't. She's seen it before. And even if she hasn't seen it, it won't surprise her any.

[spudstar99]

set N=.9(repeating)

if N=.9(repeating) then 10N=9.9(repeating)

10N-N=9.9(repeating)-.9(repeating)=9=9N

take 9N=9 and separate the N

9N/9=1

N=1

so... N=1 but N also = .9(repeating) 9N are 9*0.9(repeating)

you claimed 9N=9 that is wrong, because you claimed n=0.9 ... don't mix this ...

this is a little bit abstract but just keep an eye on the little things

so that is maybe your fault ;P

sincery spud

[spudstar99]

@ Basilikos ('index.php?page=User&userID=3376')

Sorry, but we've all seen this one before.

And yes, it's true.





http://www.dual-boxing.com/forums/../forum/icon/quoteS.png Quoted

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

And while I'm here, why is it that everyone who posts this on any given forum (and I've seen it on many) has to make it so damn complicated? Why not used the four lines I've posted above? It is just for the sake of making someone's head spin? easy 9* (1/9) = 1 not 0.9(repeating)
and 9*0.1(repeating) = 0.9(repeating)
they are not equal
just as info

[Turenn]

you guys are geeks :)

[Frosty]

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

Nerd on Nerd rage!!! RAWR!!!

[Basilikos]

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

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?

[Basilikos]

Why do I feel the need to beat you all up??? :P
Because we probably deserve it.

[spudstar99]

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

[Basilikos]

but 0.1(repeating)*9 = 1
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. Here ('http://en.wikipedia.org/wiki/0.999...') 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.

[Taliesin]

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.

[aboron]

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

[Taliesin]

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.

[Basilikos]

... 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.

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.

[Basilikos]

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

[Taliesin]

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.

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.

[Basilikos]

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.
Quoting from the article:

One can define other number systems using different rules or new objects; in some such number systems, the above proofs would need to be reinterpreted and one might find that, in a given number system, 0.999… and 1 might not be identical. However, many number systems are extensions of — rather than independent alternatives to — the real number system, so 0.999… = 1 continues to hold. Even in such number systems, though, it is worthwhile to examine alternative number systems, not only for how 0.999… behaves (if, indeed, a number expressed as "0.999…" is both meaningful and unambiguous), but also for the behavior of related phenomena. If such phenomena differ from those in the real number system, then at least one of the assumptions built into the system must break down.
True, other number systems can seem to cause problems. But it is important to note that this only means that at least one of the number systems involved has poor assumptions built into it. Furthermore, this article indicates that certain systems of this sort are merely situational extensions of the real number systems (i.e. rules modified or added for certain reasons) and thus may or may not be fitting systems in which to evaluate every problem which the usual real number system is suited for.

Just an observation.



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.
This is anything but a flamewar. To be fair, mathematics itself is quite a bit more theory tan settled fact since simple things like properties of equations rely on some assumptions that cannot be proven.

[Farleito]

Do you guys really have nothing better to do? Was your realm down or something?

[Taliesin]

Do you guys really have nothing better to do? Was your realm down or something?

LOL

No, I just find these kinds of discussions to be very interesting. Especially when there's so much controversy about it (outside the mainstream math community, at least). I'll never have any practical reason for knowing anything about it, but still fun for me to tinker with the ideas. I try not to be so nerdy, but I can't help it sometimes.

[Basilikos]

Do you guys really have nothing better to do? Was your realm down or something?

Like Tal, I enjoy this particular type of discussion. Truth be told, I'm woefully ignorant of alternative number systems, but I've not had a use for them yet. That, and it's my day off. I'm still reformatting all of my gaming machines. So yeah - I've got nothing better to do. What's really great is when I get wrath installed on every machine but my main and the installation goofs up in the middle of patching. It was so bad that the repair tool would take longer than reinstalling the game. Grrr.

[d0z3rr]

After reading this thread for several minutes, and doing several calculations, I have come up with the answer:





42.

[Taliesin]

Wrong.

41.9999...

:D

[mmcookies]

This thread made me facepalm a little...

Then again, math isn't exactly necessary to multibox.