Damo and Water need Schooling Again on 1/3

Yeah, he'll never admit that a fraction is a representation of a real number to him it is solely a "division problem"... I've already tried this, and explained it. Even my third grade (middle) daughter would be able to explain it, but according to Dixie, the only way you can express a number is decimally in base 10...

Okay nitwits... once more, we will open this topic up again. Let us clarify what exactly I have stated in the past, so that everyone is fully aware of what I said and what is being claimed I said, and how they differ dramatically.

Long ago, I made the casual comment that 1 couldn't be divided evenly by 3. Now, go get you a piece of scratch paper and work out the division problem yourself, if you have any doubts, but that is a true statement. Whenever you divide 1 into 3 parts, you are left with a remainder, forever and eternally, there will always be a remainder, it is never resolved. Since we can't use math that is unresolved, we presume the values to be equal after dividing the remainder so many times. Usually, we can divide to the nearest 100,000th, and that is close enough for any practical use we may have, although there are some things where a more accurate value is required, and we continue to divide this remainder until the remaining portion is insignificant to whatever we are applying the numbers to. We can divide a cake into three equal parts very easily, or a ruler, or a pie... in fact, we can divide anything into 3 equally perceived parts, and I have NEVER claimed otherwise. The ONLY claim I have ever made on this subject, is the FACT that 1 can't be divided equally by 3, it always produces a remainder.

Damo insists that I have said a fraction is "solely" a division problem, and I have NEVER made that statement. He correctly identifies a fraction as a "fractional representation" of a number, which is what I said... a fraction is NOT a number! Even Damo's third grade daughter should know, if you divide the numerator and denominator of a fraction, you get the actual numeric value of the fraction itself, it is, for all intents and purposes, a 'division problem' ...or as Damo stated another way... a "fractional representation" ...NOT a number!

From this argument, has spawned the silly and ridiculous notion that I have said 1/3 doesn't exist... that I have stated things can't be divided by three.... that other base math doesn't exist... and a host of other related absurdities. This is because it's what they do when they can't bring themselves to admit I am right about something. It just pains them too much to admit that, so they have to construct all of these ridiculous points I never made, and mock me over and over again. After they have repeated the lie dozens of times, people get to believing what they post... Dixie really must not believe in 1/3! But Dixie never said any such thing, never implied anything remotely close to that. It was just a simple observation of fact, that ONE can't be divided THREE times, without producing a remainder! I have repeatedly challenged the BRAINS here to give me the 3 equal values which can be added together to make 1, not the "fractional representations" and not another "division problem" but the actual numeric values I need to add together to get 1. So far, all they come up with is 1/3+1/3+1/3=1 ...which I haven't disputed.

Okay... which of you morons wants to kick off this sure to be a 2000 post thread, on this silly and ridiculous topic? Because, after all folks, debating whether 1 can be evenly divided by 3, is FAR more important for us to debate than what is currently happening in our country! Twisting Dixies words into absurd silliness is FAR more important than talking about things that effect us all as Americans. Before we can move on to debate Nationalized Health Care, the Economy, the Environment, Science, God, whatever...we must first settle this debate about 1/3, because THAT is something VERY important!
 
Long ago, I made the casual comment that 1 couldn't be divided evenly by 3. Now, go get you a piece of scratch paper and work out the division problem yourself, if you have any doubts, but that is a true statement. Whenever you divide 1 into 3 parts, you are left with a remainder, forever and eternally, there will always be a remainder, it is never resolved.

LOL. And that remainder will ALWAYS be 33333. Infinity isn't the problem you make it out to be. Anyone with a basic understanding of higher level math and the infinite series knows that and infinitely repeating decimal poses no problem.

We KNOW what 1/3 is. We KNOW what .33333e is. The fact that it repeats infinitely in decimal form isn't a problem because it repeats infinitely IN A PREDICTABLE FASHION.

Since we can't use math that is unresolved,

It's NOT unresolved. No matter how many times you divide that out it's always going to be .33333e. It's predictable. If it did not, it would not be the value 1/3. This would make a lot more sense to you if you'd ever taken calculus; I did not initially have the mathematical knowledge at first to definitively disprove you, I just knew from common sense that your statement was being counter intuitive. If you looked at and studied the mathematical proofs I'm sure you would come to the same conclusion I have.

we presume the values to be equal after dividing the remainder so many times.

We do not PRESUME, we KNOW.

Usually, we can divide to the nearest 100,000th,

We can divide however much we want, but dividing a repeating decimal like 1/3 is a redundant operation with no practical utility.

and that is close enough for any practical use we may have, although there are some things where a more accurate value is required, and we continue to divide this remainder until the remaining portion is insignificant to whatever we are applying the numbers to.

No, we multiply by the fractional notation 1/3 to obtain perfect accuracy.

We can divide a cake into three equal parts very easily, or a ruler, or a pie... in fact, we can divide anything into 3 equally perceived parts, and I have NEVER claimed otherwise. The ONLY claim I have ever made on this subject, is the FACT that 1 can't be divided equally by 3, it always produces a remainder.

1 can be divided equally into 3 parts. The fact that this produces an infite remainder is irrelevant because the remainder always repeats in a PREDICTABLE FASHION. In decimal notation you need an infinite series to represent this, but to anyone who knows the basics of calculus this is no fucking problem. We deal with infinity all the time in calculus and it has a large amount of practical applications. Something that repeats infinitely with predictable regularity is no problem at all. 1, actually, has notations that repeat infinitely. .9999e is actually just another way to say 1, just as .3333e is just another way to say 1/3.

Damo insists that I have said a fraction is "solely" a division problem, and I have NEVER made that statement. He correctly identifies a fraction as a "fractional representation" of a number, which is what I said... a fraction is NOT a number! Even Damo's third grade daughter should know, if you divide the numerator and denominator of a fraction, you get the actual numeric value of the fraction itself, it is, for all intents and purposes, a 'division problem' ...or as Damo stated another way... a "fractional representation" ...NOT a number!

A fraction is merely another way of representing a number. To claim that it is only valid as a way to express a division problem is ignorance. You do NOT need to reduce something to a decimal value for it to be a number! There are many ways to represent a number, decimal expressions and fractional expressions are just two of the most common ways! I could pull out of my ass right now a way to represent a number. The fact is that something represents a number BECAUSE WE SAY IT DOES. Decimal notation is NOT any more valid than fractional notation!

It was just a simple observation of fact, that ONE can't be divided THREE times, without producing a remainder!

Sure, 1 can't be divided into 3 without producing a wholly predictable remainder infinite in length, but this is not the grand mathematical problem you are making it out to be. It's a trivial and boring problem that was done away with by 17th century mathematicians, if not before then.
 
There are the natural numbers - like 1, 2, 3, and 4.

Then you expand that set to include decimals like 0.25 and 0.33333e. Again, the infinitely repeating nature of 0.3333e poses absolutely no problem because it repeats predictably and may be easily and accurately represented in fractional notation, or in a non-repeating form in another base, or using an infinite series, or any number of alternate notations.

Then there are irrational numbers like pi, which repeat infinitely and have no fractional notation. These numbers actually pose some of the problems that Dixie is claiming 1/3 has. But it is ignorance to say that the infinite repeating in decimal form is the problem. It's actually the inability to wholly and accurately represent the number using any system of symbolic notation at all that's the problem.
 
Long ago, I made the casual comment that 1 couldn't be divided evenly by 3. Now, go get you a piece of scratch paper and work out the division problem yourself, if you have any doubts, but that is a true statement.

sorry, but you are wrong....I took the scratch paper and a scissors and carefully cut it into three equal parts....I measured all three parts by size, weight and volume......they were all equal....
 
We can divide a cake into three equal parts very easily, or a ruler, or a pie... in fact, we can divide anything into 3 equally perceived parts, and I have NEVER claimed otherwise.

That's a flat fucking lie. God I wish the FP shit was still up.

You're lying again, as is normal, usual and routine with you. Wow A total, unequivocal, bold faced lie.

Shameful.
 
sorry, but you are wrong....I took the scratch paper and a scissors and carefully cut it into three equal parts....I measured all three parts by size, weight and volume......they were all equal....

"We can divide a cake into three equal parts very easily, or a ruler, or a pie... in fact, we can divide anything into 3 equally perceived parts, and I have NEVER claimed otherwise."
 
"We can divide a cake into three equal parts very easily, or a ruler, or a pie... in fact, we can divide anything into 3 equally perceived parts, and I have NEVER claimed otherwise."

Liar. You and I went back and forth about 50 times where you were running around claiming that they were relatively equal but not exactly equal.

You can't have it both way you total blithering fool. If you can divide 1 ruler into 3 equal parts, then you can divide one by three, equally.

And you wonder why everyone accuses you of talking out of both sides of your mouth.

You are a stubborn, utter, complete hypocritical buffoon. A joke.
 
true dat beefy.

to everyone that came late to the party, dixie is still making shit up. He does this all the time. Keep in mind he's had 4 years to work on his argument and it still sounds stupid. So just imagine it when it first started.

Dixie claimed you could not divide a cake equally into 3 parts, because it would be too hard to have AN EXACT one third cut. I remember that vividly.
 
(1) the reals are not, as the rationals are not, the maximal number
system;
(2) there exist larger number systems, containing infinitesimals;
(3) in such larger systems, the interval [0, 1] contains many numbers
infinitely close to 1;
(4) in a particular larger system called the hyperreal numbers, there
is a generalized notion of decimal expansion for such numbers,
starting in each case with an unbounded number of digits “9”;
(5) all such numbers therefore have an arguable claim to the notation
“.999 . . .” which is patently ambiguous (the meaning of
the ellipsis “. . .” requires disambiguation);
(6) all but one of them are strictly smaller than 1;
(7) the convention adopted by most professional mathematicians
is to interpret the symbol “.999 . . .” as referring to the largest
such number, namely 1 itself;
(8) thus, the students’ intuition that .999 . . . falls just short of 1
can be justified in a mathematically rigorous fashion;
(9) the said extended number system is mostly relevant in infinitesimal
calculus (also known as differential and integral calculus);
(10) if you would like to learn more about the hyperreals, go to your
teacher so he can give you further references.

http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.0164v8.pdf
 
Well that's certainly an unorthodox way to look at things.

The fact that .9999e = 1 is justified by the infinite series:

http://en.wikipedia.org/wiki/.999

Perhaps the most common development of decimal expansions is to define them as sums of [ame="http://en.wikipedia.org/wiki/Infinite_series"]infinite series[/ame]. In general:
5ad5efb99f27fda9a1cb249d7a4d299b.png


For 0.999… one can apply the [ame="http://en.wikipedia.org/wiki/Convergent_series"]convergence[/ame] theorem concerning [ame="http://en.wikipedia.org/wiki/Geometric_series"]geometric series[/ame]:[2]
If
2062d891e4922d158413d54d9e796255.png
then
5944b421545ee7150a09a891231a1855.png


Since 0.999… is such a sum with a common ratio
e3783da5d17d10e76178ddb827bd666b.png
, the theorem makes short work of the question:
56949181a290ce561f27bd550a720392.png






There are a number of algebraic proofs which are easier to understand but less convincing.
 
true dat beefy.

to everyone that came late to the party, dixie is still making shit up. He does this all the time. Keep in mind he's had 4 years to work on his argument and it still sounds stupid. So just imagine it when it first started.

Dixie claimed you could not divide a cake equally into 3 parts, because it would be too hard to have AN EXACT one third cut. I remember that vividly.

No, I said that you have not proven you can do this, and you haven't. If you could give me the precise equal percentages of each slice of cake, I will accept that... but we know you can't do that either, can you?
 
No, I said that you have not proven you can do this, and you haven't. If you could give me the precise equal percentages of each slice of cake, I will accept that... but we know you can't do that either, can you?

I like how you think you're being clever by demanding percentages, as if the cake can only be divided into three if that number can be represented in percentage notation without a repeating decimal (which is an mathematically ignorant point of view). It's another case of that strictly conservative worldview, where you develop a (usually incorrect) model and demand that reality change in order to fit this incorrect model. Nevertheless, I will oblige you.

Each slice of cake is exactly 1/3 of 100%. Or 33.3333e% of 100%, which is the exact same value. That is the precise, equal percentage of each slice of cake.
 
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No, I said that you have not proven you can do this, and you haven't. If you could give me the precise equal percentages of each slice of cake, I will accept that... but we know you can't do that either, can you?

Can 1 ruler be divided into 3 exact;y equal parts?
 
"We can divide a cake into three equal parts very easily, or a ruler, or a pie... in fact, we can divide anything into 3 equally perceived parts, and I have NEVER claimed otherwise."

Dixie....here is the rub....we can divide one into three equal parts, we just cannot express that fact using the decimal system......three 1/3 sections equal 1.....fractions work fine.....
 
lol....i don't trust dixie....he claims to not have said or claimed something and when you show him he said it....he runs away

Ha, this never gets old! But to be fair, it’s the reason Dixie is more fun than a barrel of monkeys! Apparently he periodically forgets the board has a search function....bummer!


Posted by CYPRESS:

"Dixie, you're on record saying that if it were up to you, women who get abortions should be stoned to death. Your words. You're on record with that."

Posted by DIXIE:

“Again you misinterpreted something I said and took it out of context to insist I said something I did NOT say! You do this all the time, and everyone me and some rightwing extremists on this board with an ounce of honesty obsession know you do it.

So continue to spew your LIES, that is all you are good for.”

POSTED BY DIXIE. 2006:

"If it were up to me personally, there would be no legal abortion... If any abortion occurred for any reason, it would be a crime of murder, punishable by death, preferably stoning, as God mandated in the Old Testament..... I merely made the point that I don't expect society to live by my personal beliefs, or our laws to be structured around what I personally believe”

…."My exception for rape and incest is a compromise, it doesn't mean I am a hypocrite, my personal view is not important, and I wouldn't expect society to conform to what I personally think, if I thought that was appropriate, I would advocate against all abortion and recommend stoning... IF it were up to me alone to decide. I hope that you can comprehend the context of what I stated…."

http://www.justplainpolitics.com/sho...&postcount=152
 
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