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Geek Culture / Is 10 = 9.9999999... ??

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Mahoney
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Posted: 24th Aug 2008 03:18
Quote: "You're saying maths and science are both theories?"


I'm saying the Big Bang is a theory, not science. I was simply making a correction to your wording. I wasn't trying to contend your statement.

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dark coder
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Posted: 24th Aug 2008 03:27
There's nothing wrong with my wording, he cited unsolved math problems as proof that maths was flawed, I showed a scientific theory that wasn't fully understood/unsolved(like the math ones) thus was asking if he believed science to be flawed because of this. I could also cite many other unsolved scientific problems, but no matter how long my list, it will never make science flawed in any way. The ways at which the science at hand is studied can be flawed, the models we propose govern something can be flawed, but the study of natural phenomena, aka science is not because of this.

Mahoney
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Posted: 24th Aug 2008 04:39
In that case, sorry. I misread your statement.

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Super Nova
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Posted: 24th Aug 2008 07:07
1/3 does not equal .333 even if you add infinite 3's. 1/3 cannot be represented in any decimal(just try to find one that actually equals 1 when multiplied 3 times). You cannot represent all numbers in decimals. That being said, .333^infinity is the closest a decimal can get to 1/3, but that does not make it 1/3.

This is why learing fractions in school is important because decimals are just inaccurate representations of fractions. We only use decimals to make our understanding of math and fractions easier.

Well, this is how I always thought of it anyway.

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Sid Sinister
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Posted: 24th Aug 2008 07:24
Can anybody say NERDS!? *cough*



Seriously guys... there are better things in life than numbers. The only number that counts is two, and if your missing one (or both for that matter), then your done for.

"If I have seen a little further it is by standing on the shoulders of Giants" - Isaac Newton
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ionstream
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Posted: 24th Aug 2008 08:19
Quote: "1/3 does not equal .333 even if you add infinite 3's."


Yes it does. Read the geometric series proof above.

Quote: "You cannot represent all numbers in decimals."


Not irrational ones at least, but rational ones like 1/3 and 1/9 you definitely can.

Geryon
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Posted: 24th Aug 2008 08:22 Edited at: 24th Aug 2008 08:27
Somehow, I think the topics like this on GameFAQs have smarter people. At least, the trolls on CE who act like they don't know what they're talking about don't present arguments that make it look like they're trying to be serious.

If someone here doesn't understand why 1 = 0.999~, they should be banned for being under 13 years old. Here's two arguments that even someone 13 years old could understand.

First:
Write out 1/3 in decimal form.
Write out 2/3 in decimal form.
Write out 3/3 in decimal form.
???
PROFIT!

Second:
For two numbers to be different, there has to be some number between them, right? Can anyone name a number that falls between 0.999~ and 1? Anyone? No? >_>

Quote: "So...again, is 1.0 the same as 0.999, because I'm seeing 2 different values."


Here's a reason that numbers have multiple representations:

4
4.0
2+2

Do you consider the above three representations of 4 to be different values? I didn't think so. Why are you so closed-minded when it comes to representing 4 as 3.999~?


[EDIT
Quote: "You cannot represent all numbers in decimals."


You cannot fully represent all numbers in decimals. But you can certainly approximate all numbers in decimals. There's even a start to things like the decimal approximations of e and pi.

Also, whoever posted above me: Irrational numbers cannot be represented as the quotient of two integers. But they've all got approximate decimal forms.

Actually, what I said above may be inaccurate. You can't represent i in decimal form. But 0.999~ is not imaginary, so that's beside the point.
</edit>
---------------------------------------------------------------

And one last note: If you don't consider yourself good at mathematics, just leave the thread.
RedneckRambo
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Posted: 24th Aug 2008 08:47
Why can't we all just come to the conclusion that math is flawed? Especially with the fact that we've already established that conclusion.

ionstream
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Posted: 24th Aug 2008 09:06 Edited at: 24th Aug 2008 09:11
Quote: "Why can't we all just come to the conclusion that math is flawed?"


Because it's not, not by a lot. You can't say that the system is flawed just because you don't understand it, what you should be asking is why don't you understand it.

Quote: "Especially with the fact that we've already established that conclusion."


The only conclusion we have come to is the 3 ways to prove that 0.9~ is 1.

Quote: "Actually, what I said above may be inaccurate. You can't represent i in decimal form."


I just meant non repeating numbers like pi and e can't be represented with a decimal (or fraction for that matter) even with the bar symbol, but they can be approximated with them.

Edit: Does anyone here use the bar notation? I think I'm the only one, maybe it's an outdated way to do it :/ . I've always seen an infinite repeating decimal to have a bar over the repeating part, but Wikipedia doesn't seem to use that notation. Maybe it's a United States thing!

RedneckRambo
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Posted: 24th Aug 2008 09:25 Edited at: 24th Aug 2008 09:26
Quote: "Because it's not, not by a lot. You can't say that the system is flawed just because you don't understand it, what you should be asking is why don't you understand it."

No, it's flawed.

Edit- I used the bar.

Seppuku Arts
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Posted: 24th Aug 2008 13:12
Quote: "Why are you so closed-minded when it comes to representing 4 as 3.999~?"


Because I haven't been given an explanation as to why 4 isn't actually 4 that makes sense.

Quote: "First:
Write out 1/3 in decimal form.
Write out 2/3 in decimal form.
Write out 3/3 in decimal form.
???
PROFIT!"


Surely fractions can't be represented in decimal form, this is why people are say it's flawed - changing '1' to equal 0.999 only allows for those fractions to work. 0.333 is the closest to a third that a decimal number can be surely. 0.999 isn't a whole number is it? I dunno, but it just seems to be illogical that a number can equal a number less than itself. Like I said in a previous example (applying to objects): I have 1 mouse, is it only very slightly not 1 mouse?

You sir have the moral ambivalence of a mutated shrimp!
dark coder
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Posted: 24th Aug 2008 13:13
Quote: "Can anybody say NERDS!? *cough*

Seriously guys... there are better things in life than numbers. The only number that counts is two, and if your missing one (or both for that matter), then your done for. "


You're right, why don't we talk about crap like baseball and NASCAR, maths is far too uncool. Oh snap, 99% of topics and threads on this board are 'nerd' related, looks like your post count will be really high once you notice this.

Green Gandalf
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Posted: 24th Aug 2008 14:32
This thread is painful to read.

The number "9.9999..." (i.e. the 9's repeatedly infinitely) has a value equal to the infinite limit of the sequence

9.9
9.99
9.999
9.9999
9.99999
(etc)

which is of course 10. What's the problem?

Quote: "I dunno, but it just seems to be illogical that a number can equal a number less than itself."


Quite right. But "9.9999999999999999999 ... (etc)" is just a silly clumsy way of writing "10".

While we're at it, in binary notation, "1.111111111111111 ... (etc)" is just an equally silly way of writing "10".
tha_rami
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Posted: 24th Aug 2008 15:04 Edited at: 24th Aug 2008 15:09
Wait, so basically, the problem then is in
Quote: "1/3=0.333..."

Which is an estimate, because there is no such thing as infinite, thus not an exact.

But then:
1/3 * 3 = 1
1/3 roughly equals 0.333...?
Because 0.333...*3 <> 1

And how about: 1/3^1000... <> 0.333...^1000...?
(where 1000... is 1000 with infinite zeros after it)


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Green Gandalf
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Posted: 24th Aug 2008 15:29
Quote: "Which is an estimate, because there is no such thing as infinite, thus not an exact."


It is not an estimate - it's one correct way to express 1/3 in decimal notation. No more, no less.

Quote: "And how about: 1/3^1000... <> 0.333...^1000...?
(where 1000... is 1000 with infinite zeros after it)"


Both are zero of course. What's the problem?
Benjamin
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Posted: 24th Aug 2008 16:14
Quote: "If someone here doesn't understand why 1 = 0.999~, they should be banned for being under 13 years old."

If someone doesn't agree with me they should be banned.

I don't agree with it.

Mahoney
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Posted: 24th Aug 2008 16:38
Quote: "I don't agree with it."


Benjamin, I'm surprised. Your one of the smartest people on this forum. Why is it that you don't agree with it.

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Benjamin
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Posted: 24th Aug 2008 16:52 Edited at: 24th Aug 2008 16:54
Oh, I'm sorry, I'm not allowed my own view on it? I guess I interpreted the reason for this thread existing wrong. Wait, it has a reason?

I just don't believe absolution can be achieved by adding a fraction an infinite amount of times. Intelligence doesn't factor into this anyway, you're thinking of knowledge.

BiggAdd
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Posted: 24th Aug 2008 16:58
Surely it is more correct to say 0.999... tends to 1, rather than saying it is equal to 1?

Seppuku Arts
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Posted: 24th Aug 2008 17:05 Edited at: 24th Aug 2008 17:08
Just because somebody is smart it doesn't mean that they have to agree with other smart people.

But it seems thirds of '1' cannot be accurately represent by decimals: 0.333~ is the closest, but it isn't exactly a third, which is why you get 0.999~ when times by 3 right?

0.999~ seems to be just an adjustment to deal with it, but 0.999~ isn't exactly the same as 1.0, am I correct?

Again with the logic a number can't be less than itself, 1.0 can only literally be 1.0 (or 10.0 as 10.0)

You sir have the moral ambivalence of a mutated shrimp!
Green Gandalf
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Posted: 24th Aug 2008 17:19 Edited at: 24th Aug 2008 17:20
Quote: "but 0.999~ isn't exactly the same as 1.0, am I correct?"


No, you are not correct. Every single number in the sequence

0.9
0.99
0.999
0.9999
0.99999
(etc ad infinitum)

is different from 1. But the limit of that sequence, which could be written as "0.999...", is nothing more or less than 1. It's just a long-winded way of writing 1.

You lot are making a meal of this.
Benjamin
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Posted: 24th Aug 2008 17:21 Edited at: 24th Aug 2008 17:25
Bah...

Note that this 'bah' extends to infinity thus is proof.

Quote: "It's just a long-winded way of writing 1."

I think it's more like a number that is infinitely close to 1.

tha_rami
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Posted: 24th Aug 2008 17:37
Quote: "Both are zero of course. What's the problem? "

That is assuming the theory is correct, which, as far as I'm concerned, it isn't.

Benjamin pretty much said it:
Quote: "I think it's more like a number that is infinitely close to 1."



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Seppuku Arts
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Posted: 24th Aug 2008 17:56
There you go: 'one of the smartest' people on the forum has made a statement I think makes most sense.

You sir have the moral ambivalence of a mutated shrimp!
Agent Dink
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Posted: 24th Aug 2008 18:08 Edited at: 24th Aug 2008 18:15
Just as the frog jumping across half the distance of the remaining log each time he jumps will never reach the end of the log, so will 10 never actually = 9.9repeating.

It is extremely close to being equal, but really it's never going to be.

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IanM
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Posted: 24th Aug 2008 18:24
Quote: "What's the problem?"

The problem is that all these 'laymen' believe the experts are not only wrong, but have been wrong for 100's of years, and that no-one seems to have noticed

I'm a layman myself. I've only understood a very few of the proofs I've seen (fractions & algebraic for example) and I can't see any logical failing of them.

Quote: "Note that this 'bah' extends to infinity thus is proof"

Yeah, well back at you, infinity plus 1... darn, that doesn't work, 'cos infinity+1 = infinity apparently.

However, perhaps that's where people are falling down on this - when you involve infinity the rules aren't the same as your 'gut feelings' require.

Benjamin
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Posted: 24th Aug 2008 19:58 Edited at: 24th Aug 2008 20:04
Well, until it's useful for me to believe that 0.999... is the same as 1, I'll stick to my wrong viewpoint for now.

Well you stick to your theoretical, intangible numbers, while I rely on something more concrete.

IanM
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Posted: 24th Aug 2008 20:52
'There ain't no such animal' - man upon seeing a giraffe for the first time.

I've seen several proofs offered by others, but not yours that they're wrong.

There's the chance you are right, and if that's the case I'll happily say you were right and everyone else, including me, was wrong - just prove it first.

Green Gandalf
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Posted: 24th Aug 2008 20:57
Quote: "Just as the frog jumping across half the distance of the remaining log each time he jumps will never reach the end of the log, so will 10 never actually = 9.9repeating."


You've confused the infinite number of jumps the frog takes with the finite distance he jumps overall - and that is 10 (assuming the first jump were 5 units).

And how much time he takes for each jump hasn't been specified at all so it's anyone's guess whether he actually reaches the end in a finite time.
RedneckRambo
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Posted: 24th Aug 2008 21:09
Everyone here is arguing that a non existent number is equal to an existent number. .9999.... doesn't exist.

Mahoney
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Posted: 24th Aug 2008 21:24
Quote: "Oh, I'm sorry, I'm not allowed my own view on it? I guess I interpreted the reason for this thread existing wrong. Wait, it has a reason?"


I'm not sure how what I said was interpreted, but I was merely asking your opinion (and giving you a compliment!). Sorry if I offended you.

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Agent Dink
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Posted: 24th Aug 2008 21:33
Quote: "
You've confused the infinite number of jumps the frog takes with the finite distance he jumps overall - and that is 10 (assuming the first jump were 5 units).

And how much time he takes for each jump hasn't been specified at all so it's anyone's guess whether he actually reaches the end in a finite time. "


How can you reach the end of something when you only travel half the distance remaining each time you move. If there is an inch of log left, the frog can only jump 1/2 of an inch. Then half of 1/2 inch (1/4 inch), then half of 1/4 inch (1/8 inch). But after each of those jumps he is always left with the distance he just jumped in front of him. As long as there is no limit to numbers and some sort of minimum distance a physical object can travel in our universe there will always be some little fragment of log left he must jump. To the human eye it will appear he has reached the end, but he never will. There will always be a gap between him and the edge. Just as there will always be the ever so tiniest gap between 1 and 0.9repeating.

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Peter H
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Posted: 24th Aug 2008 21:38
"Is 10 = 9.9999999... ??"
no

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Agent Dink
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Posted: 24th Aug 2008 21:44
10 cannot equal 9.9 repeating because there will always be that 0.0...repeating...001 leftover.

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Green Gandalf
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Posted: 24th Aug 2008 21:48
Quote: ""Is 10 = 9.9999999... ??"
no"


What's the difference exactly?


Quote: "As long as there is no limit to numbers and some sort of minimum distance a physical object can travel in our universe there will always be some little fragment of log left he must jump."


Rubbish fortunately.

Consider a more concrete example (which some of you seem to be demanding):

A bullet travels at, say, 5000 cm per second. In the next 1/2 second it travels 2500 cm, in the next 1/4 sec it travels 1250 cm, and so on. Using your argument it couldn't possibly travel more than 10000 cm (= limit of 5000 + 2500 + 1250 + 625 + (etc ad infinitum) - which is absolute nonsense of course. It takes 2 secs to reach 10000 cm and the bullet continues (unless it hits a concrete wall of misunderstanding ).
Geryon
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Posted: 24th Aug 2008 22:00
Quote: "10 cannot equal 9.9 repeating because there will always be that 0.0...repeating...001 leftover."


Finally...this argument. I was about to bring this up myself, and subsequently show why it doesn't make sense.

If I give you 0.0, and I tell you to add a 1 to the end of that, you'll show me 0.01. And we could continue this...

0.1
0.01
0.001
0.0001
0.00001
0.000001
et cetera...

Now, we can also represent these as...
1-0.9
1-0.99
1-0.999
1-0.9999
1-0.99999
1-0.999999
et cetera...

But when we get to an infinite string of 9's after that decimal point, we end up with
1-0.9999999999999999999999999999999999999999999999~

Now, that's an infinite, never-ending string of nines on the end of that second number up there. So, when you perform the subtraction, you would expect 0.000000~1. Listen very carefully to the next three words of this post:

THAT. DOESN'T. WORK!

If you perform the subtraction of 1-0.999~, you have an infinite string of zeroes to deal with in the resulting decimal number. Where is the "end" that you're so eager to tack the 1 onto? There is no such ehd; it doesn't exist because of the infinite number of zeroes. But if there's no end to the zeroes, then the resulting difference is 0.000~, a number which I'm sure everyone in this thread will agree is exactly equal to zero. There is no 1 on the end of that because the end that you want to put your 1 on doesn't exist. And how can you place something at a non-existent position?

But wait! That means that 1-0.999~ = 0. If you were to add 0.999~ to both sides, you end up with 1 = 0.999~.

Any questions, class?
RedneckRambo
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Posted: 24th Aug 2008 22:05 Edited at: 24th Aug 2008 22:06
[edit] This is stupid.

Insanity Complex
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Posted: 24th Aug 2008 22:09
Quote: "And how can you place something at a non-existent position?"


How can you subtract an infinite number, from a finite number, and claim it results in a finite number? I'm not the greatest at math...but seriously...


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Geryon
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Posted: 24th Aug 2008 22:13
Quote: "How can you subtract an infinite number, from a finite number, and claim it results in a finite number? I'm not the greatest at math...but seriously..."


0.999~ is not infinite. It is equal to 1. It just takes an infinitely long string of numbers to write out.

Do you also consider pi and e to be infinite?
Insanity Complex
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Posted: 24th Aug 2008 22:16
If it's equal to 1 why does it exist as .999~

xD I really should stay out of math threads


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Green Gandalf
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Posted: 24th Aug 2008 22:25
Quote: "I really should stay out of math threads"


You aren't the only one.
Geryon
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Posted: 24th Aug 2008 22:29
Quote: "If it's equal to 1 why does it exist as .999~"


It's just a provable, mathematical fact that 0.999~ = 1. It's been proven several times in this thread, and the people arguing against it all seem to make the same mistake. They treat infinity as a finite value, which can't be done. If 0.999~ had a finite number of nines, then yes, there would be a string of zeroes with a 1 on the end when you subtracted 0.999~ from 1. But that's not the case. There's an infinite string of nines, so when you subtract it from 1, you get an infinite string of zeroes, to which there is no end, so there is no room for a 1 on the end of it.

That's why treating infinity as though it were finite doesn't work.
Benjamin
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Posted: 24th Aug 2008 22:34
Quote: "I'm not sure how what I said was interpreted, but I was merely asking your opinion (and giving you a compliment!). Sorry if I offended you."

It's my fault, my post was more in response to the attitudes of others.

Quote: "There's the chance you are right, and if that's the case I'll happily say you were right and everyone else, including me, was wrong - just prove it first."

I don't have to prove it to believe it.

Mr Tank
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Posted: 24th Aug 2008 22:58
Yes.

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Mahoney
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Posted: 24th Aug 2008 23:14
Quote: "It's my fault, my post was more in response to the attitudes of others."


Alright. I thought that I had made you mad.

Quote: "But when we get to an infinite string of 9's after that decimal point, we end up with
1-0.9999999999999999999999999999999999999999999999~

Now, that's an infinite, never-ending string of nines on the end of that second number up there. So, when you perform the subtraction, you would expect 0.000000~1. Listen very carefully to the next three words of this post:

THAT. DOESN'T. WORK!

If you perform the subtraction of 1-0.999~, you have an infinite string of zeroes to deal with in the resulting decimal number. Where is the "end" that you're so eager to tack the 1 onto? There is no such ehd; it doesn't exist because of the infinite number of zeroes. But if there's no end to the zeroes, then the resulting difference is 0.000~, a number which I'm sure everyone in this thread will agree is exactly equal to zero. There is no 1 on the end of that because the end that you want to put your 1 on doesn't exist. And how can you place something at a non-existent position?

But wait! That means that 1-0.999~ = 0. If you were to add 0.999~ to both sides, you end up with 1 = 0.999~."


Hopefully, most will understand this now. It should end the "What about the 0.00~1?" argument, at least. But, I'm sure there are other points that can be made against the theory.

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Cash Curtis II
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Posted: 24th Aug 2008 23:19
I didn't believe this at all when I first saw this thread. Then I read the Wikipedia article and still wasn't comfortable with it. It said in the article that most students aren't comfortable with the concept when they are exposed to it. But then I followed the algebraic proof on the page and it made perfect sense.


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Mahoney
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Posted: 24th Aug 2008 23:22 Edited at: 25th Aug 2008 02:58
Quote: "I didn't believe this at all when I first saw this thread. Then I read the Wikipedia article and still wasn't comfortable with it."


Same here. It took a bit. It takes awhile to really grasp the concept of infinity, and actually apply it to your thoughts. When you do, it makes perfect sense; and it's pretty awesome, in my personal opinion.

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tha_rami
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Posted: 25th Aug 2008 01:25
Well, luckily for me 0.999... doesn't exist, cause I still don't buy it. I'll teach my kids to count 0, 1, 2, 3 instead of 0, 0.999..., 1.999..., 2.999....

For me, what Benjamin said still makes the most sense: 0.999... is infinitely close to 1, and like Adam said, the frog never reaches the end, even if it jumps for infinity.


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RalphY
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Posted: 25th Aug 2008 02:43
Interesting, all the proofs given so far make sense so it would seem mathematically 0.9... = 1. I'm with Cash on this one, having read the proofs given on the wiki page it makes perfect sense.

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Aaron Miller
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Posted: 25th Aug 2008 03:35 Edited at: 25th Aug 2008 03:55
0.999~ can be used to REPRESENT 1.0, but it's not. There is a small difference between them but it can't be represented in decimal. 0.999~ is not the same as 1, there is an infinitely small difference between them.

EDIT
Quote: "And how can you place something at a non-existent position?"

Infinity doesn't exist, how can you place the last 9? More seriously though, just like this: 0.000~1 meaning that the last number after infinity will be 1. Like so:

0.001
0.0001
0.00001
0.000001
0.0000001

And so on.

It looks like this conversation isn't going anywhere, and no one is accepting any one's point of view except theirs. I'm not going to change my mind because someone gives an example of a bullet reaching somewhere else, or providing idiotic proof that 0.999~ is 1.0. It doesn't work like that.

If there's an infinite series of 9s then how come 1.0 has no infinite series of anything?

Cheers,

-naota

I'm not a dictator to those that do stuff for me by will. Only those who don't.

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