zonhin
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It was a mistake on his part. Sometimes people aren't clear, and it can seem like they mean something completely different then what they say.

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eytanz
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zonhin wrote:
It was a mistake on his part. Sometimes people aren't clear, and it can seem like they mean something completely different then what they say.

So, er, what did he actually mean?

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eytanz
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Ok, to answer my own question, after reading all his posts it seems to me that Syntax's position is the following:

1. Math has two ways of referring to numbers - transformations and representations.

2. In his opinion, no number can have more than one representation.

3. He does not consider 1 and 0.9999.... to be transformations, and therefore, by [1], they are both representations. By [2], they cannot be representing the same number.

4. If you put the equal sign between two representations, then they have to be the same in order for the formula to be valid.

5. By [3] and [4], 1=0.9999.... is not vaid.

Is that a fair paraphrase of Syntax's view?

Note that the italicized parts are taken directly from his posts.

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[Last edited by eytanz at 02-03-2008 11:38 AM]

Syntax
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I was trying to stay out of this subject, but here's my last point anyway (though I'm quite proud of the fact my statements have caused a discussion)...

I do not agree with the fact 1 = .999...

Full stop.

Sillyman
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You are WRONG, dear sir. You cannot disagree with a fact. 1 = .9 repeating, whatever your opinion may be. Therefore, I shall be forced to mod you down for horrendous logic. Good day.

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Syntax
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I do believe the title of this thread asked:
"Believe it or not"

I chose not to.

zonhin
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eytanz wrote:

zonhin wrote:
It was a mistake on his part. Sometimes people aren't clear, and it can seem like they mean something completely different then what they say.

So, er, what did he actually mean?

I dunno.

Anyway, Syntax, stop being disagreeable. Seriously. This is silly. And everything else that's going on is silly.

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golfrman
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zonhin wrote:
And everything else that's going on is silly.

Just since sillyman posted.

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Sillyman
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Hey, I can be serious. But yeah, I'm usually silly. Hence the name. And Syntax is still wrong. Whether he believes it or not, 1=.9 repeating.

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[Last edited by Sillyman at 02-03-2008 10:51 PM]

Tahnan
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Syntax wrote:
I do not agree with the fact 1 = .999...

I still don't understand. 1 = .9999... is a true statement. You're saying that, in spite of various proofs given here, you don't believe it's true? And: given that I can't help reading it as "I don't agree that grass is green", can you explain why you don't believe it? (Is Eytanz's post correct?)

Jatopian
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You know, Tahnan, you should really compare it to a truism that is actually always true. There are non-green varieties of grass.

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zex20913
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To add a new wrinkle to the discussion, this fact has made me question the process of "rounding".

To "round" a number to a desired place value, look at the place value immediately to the right. If that digit is between 0 and 4 inclusive, truncate everything after the desired place value.

If the digit to the right of the desired place value is between 5 and 9 inclusive, add 1 to the digit in the desired place value, and truncate everything to the right of that digit.

For most numbers, rounding is easy. But then...

How would one round .149999999... to the nearest tenth? By the algorithm described above, one would necessarily round it to ".1".

Yet, we know that this number is equivalent to ".15" which rounds to ".2".

This is more of a qualm with the rounding algorithm than the 1=.(9) fact. But I *could* see a form of math where this is disallowed. Not that I'd believe it. There are a host of other problems that would arise from allowing it.

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zonhin
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.88888888... equals .9

I will stand by this. I don't care what you guys say. It's true.

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zex20913
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It is in base nine.

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Schik
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Nah, in base 9 it's 1.

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zex20913
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Gotcha. If ten tenths is one, so is nine ninths in base nine. They're equivalent.

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coppro
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Wikipedia wrote:
The students' reasoning for denying or affirming the equality is typically based on one of a few common erroneous intuitions about the real numbers; for example that each real number has a unique decimal expansion, that nonzero infinitesimal real numbers should exist, or that the expansion of 0.999… eventually terminates.

Emphasis mine.

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[Last edited by coppro at 02-04-2008 06:18 AM]

Znirk
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zex20913 wrote:
Gotcha. If ten tenths is one, so is nine ninths in base nine.

So's nine ninths in any base.

mrimer
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All your base are a lie.

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... This thread has degraded to the point where I'm expecting Banjooie or Snacko to post.

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zonhin
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Sillyman wrote:
... This thread has degraded to the point where I'm expecting Banjooie or Snacko to post.

Degraded?

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Sillyman
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Degraded.

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Jatopian
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Indeed. Any worse and I'll support locking it. And I /hate/ it when threads get locked.

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Znirk
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Sillyman wrote:
... This thread has degraded to the point where I'm expecting Banjooie or Snacko to post.

... "or"?

Timo006
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This is a proof given by my sister, she is studying Physics at the university of Antwerp.

Imagine a very small positive number e (e =/= 0). The difference between 1 and 0.9999... is always smaller than this number e. This counts for every number e you can imagine, so (1 - 0.999...) = 0. This means 0.999... = 1.

You can proove this also in a different way:
1/3 = 0.333... => 3/3 = 0.999....
We also know 3/3 = 1, so 0.999... = 1


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Banjooie
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It's the exact same thread that played itself so many times on the World of Warcraft forum, it became a banned topic right along religion and politics.

Seriously, anything I post in here is not going to be any better than you guys getting absolutely furious and livid at each other over a hypothetical math question.

Mattcrampy
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Sir, you offend my sense of reason!

I challenge you to fisticuffs on the field of battle!

Preferably Ruins of Lordaeron!

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Tahnan
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Banjooie wrote:
...you guys getting absolutely furious and livid at each other...

It doesn't make me furious or livid. Just sad.

eytanz
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Tahnan wrote:

Banjooie wrote:
...you guys getting absolutely furious and livid at each other...

It doesn't make me furious or livid. Just sad.

Yeah - I'm not sure I saw much fury or, er, lividity going on here. Or, for that matter, any. Mostly confusion and some lamentation, I think.

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Rabscuttle
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It's not a hypothetical question.

At least, no more than any mathematical question is hypothetical.