zonhin
Level: Delver

Rank Points: 99
Registered: 10-18-2005
IP: Logged

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.

____________________________
I looked at the world through apple eyes
And cut myself a slice of sunshine pie
I danced with the peanut butterflies
Till time went and told me to say hello but wave goodbye

eytanz
Level: Smitemaster

Rank Points: 2708
Registered: 02-05-2003
IP: Logged

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 got my avatar back! Yay!

eytanz
Level: Smitemaster

Rank Points: 2708
Registered: 02-05-2003
IP: Logged

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.

____________________________
I got my avatar back! Yay!

---

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

Syntax
Level: Smitemaster
Rank Points: 1218
Registered: 05-12-2005
IP: Logged

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
Level: Smiter

Rank Points: 339
Registered: 09-08-2006
IP: Logged

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.

____________________________
Who, me?
FNORD

Syntax
Level: Smitemaster
Rank Points: 1218
Registered: 05-12-2005
IP: Logged

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

I chose not to.

zonhin
Level: Delver

Rank Points: 99
Registered: 10-18-2005
IP: Logged

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.

____________________________
I looked at the world through apple eyes
And cut myself a slice of sunshine pie
I danced with the peanut butterflies
Till time went and told me to say hello but wave goodbye

golfrman
Level: Master Delver

Rank Points: 165
Registered: 07-10-2006
IP: Logged

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

Just since sillyman posted.

____________________________
Jesus is Lord and Messiah!

Sillyman
Level: Smiter

Rank Points: 339
Registered: 09-08-2006
IP: Logged

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.

____________________________
Who, me?
FNORD

---

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

Tahnan
Level: Smitemaster

Rank Points: 2460
Registered: 11-14-2005
IP: Logged

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
Level: Smitemaster
Rank Points: 1842
Registered: 07-31-2005
IP: Logged

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

____________________________
DROD has some really great music.
Make your pressure plates 3.0 style!
DROD architecture idea generator

zex20913
Level: Smitemaster

Rank Points: 1723
Registered: 02-04-2003
IP: Logged

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.

____________________________

zonhin
Level: Delver

Rank Points: 99
Registered: 10-18-2005
IP: Logged

.88888888... equals .9

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

____________________________
I looked at the world through apple eyes
And cut myself a slice of sunshine pie
I danced with the peanut butterflies
Till time went and told me to say hello but wave goodbye

zex20913
Level: Smitemaster

Rank Points: 1723
Registered: 02-04-2003
IP: Logged

It is in base nine.

____________________________

Schik
Level: Legendary Smitemaster

Rank Points: 5423
Registered: 02-04-2003
IP: Logged

Nah, in base 9 it's 1.

____________________________
The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi

zex20913
Level: Smitemaster

Rank Points: 1723
Registered: 02-04-2003
IP: Logged

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

____________________________

coppro
Level: Smitemaster
Rank Points: 1309
Registered: 11-24-2005
IP: Logged

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.

---

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

Znirk
Level: Smitemaster

Rank Points: 613
Registered: 07-28-2005
IP: Logged

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

So's nine ninths in any base.

mrimer
Level: Legendary Smitemaster

Rank Points: 5145
Registered: 02-04-2003
IP: Logged

All your base are a lie.

____________________________
Gandalf? Yes... That's what they used to call me.
Gandalf the Grey. That was my name.
I am Gandalf the White.
And I come back to you now at the turn of the tide.

Sillyman
Level: Smiter

Rank Points: 339
Registered: 09-08-2006
IP: Logged

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

____________________________
Who, me?
FNORD

zonhin
Level: Delver

Rank Points: 99
Registered: 10-18-2005
IP: Logged

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

Degraded?

____________________________
I looked at the world through apple eyes
And cut myself a slice of sunshine pie
I danced with the peanut butterflies
Till time went and told me to say hello but wave goodbye

Sillyman
Level: Smiter

Rank Points: 339
Registered: 09-08-2006
IP: Logged

Degraded.

____________________________
Who, me?
FNORD

Jatopian
Level: Smitemaster
Rank Points: 1842
Registered: 07-31-2005
IP: Logged

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

____________________________
DROD has some really great music.
Make your pressure plates 3.0 style!
DROD architecture idea generator

Znirk
Level: Smitemaster

Rank Points: 613
Registered: 07-28-2005
IP: Logged

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

... "or"?

Timo006
Level: Smitemaster

Rank Points: 526
Registered: 07-19-2006
IP: Logged

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


____________________________
Drod Number: 3034; 8th person to see the Second Sky

Banjooie
Level: Smitemaster

Rank Points: 1645
Registered: 12-12-2004
IP: Logged

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
Level: Smitemaster

Rank Points: 2388
Registered: 05-29-2003
IP: Logged

Sir, you offend my sense of reason!

I challenge you to fisticuffs on the field of battle!

Preferably Ruins of Lordaeron!

____________________________
What do you call an elephant at the North Pole?

Tahnan
Level: Smitemaster

Rank Points: 2460
Registered: 11-14-2005
IP: Logged

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

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

eytanz
Level: Smitemaster

Rank Points: 2708
Registered: 02-05-2003
IP: Logged

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.

____________________________
I got my avatar back! Yay!

Rabscuttle
Level: Smitemaster

Rank Points: 2502
Registered: 09-10-2004
IP: Logged

It's not a hypothetical question.

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