.999... = 1

[TheProwler]

so does .8999999999999... equal .9?

Of course.

If you incorrectly apply algebraic rules that are meant for real numbers to non-real numbers.

It's all an attempt by the pencil manufacturers to get you to use more pencils. Why write 0.9 when you can write 0.89999999999999999999999999999999?

[TheProwler]

Wait... I read these things. Is 1/9 really 0.999999999 etc.?

Nah, sully just made a big mistake which I called attention to way before prowley did.

Give yourself a Gold Star. I'm just catching up here...



I was 0.99999recurring of an infinite amount of time behind you.

[TheProwler]

Think of it as
10x - x = 9.00000...0000001

but it isn't.

0.9999... and 9.9999... have the SAME number of places after the decimal, so each one cancels out the other, when they are subtracted. THERE IS NO REMAINDER.

Haha, now you are defining infinity as a real number. "the SAME number"

So should we also say that in this equation, y = 1/x, that when x equals infinity (haha, x equals infinity), y=0? Don't answer that...I think we'd be into a whole new (and related) subject with people not understanding the limitations of performing basis algebra on non-real numbers.

Actually, Timminz is so motherfucking right it isn't even funny anymore. Infinity is always the same.

also yeah, y= 1/x with x being infinity does make y=0. Not that you didn't know that, but I always like to tell trolls facts.

Once again, you are mistaking "equals" for "approaches".

Gotta add to this....

So when x gets just a little bit bigger....does y get just a little more zero? Hahaha!!

[SultanOfSurreal]

so does .8999999999999... equal .9?

Of course.

If you incorrectly apply algebraic rules that are meant for real numbers to non-real numbers.

uh in what way is .8999... not a real number

[owheelj]

Students of mathematics often reject the equality of 0.999… and 1, for reasons ranging from their disparate appearance to deep misgivings over the limit concept and disagreements over the nature of infinitesimals. There are many common contributing factors to the confusion:
Students are often "mentally committed to the notion that a number can be represented in one and only one way by a decimal." Seeing two manifestly different decimals representing the same number appears to be a paradox, which is amplified by the appearance of the seemingly well-understood number 1.[33]
Some students interpret "0.999…" (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity".[34]
Intuition and ambiguous teaching lead students to think of the limit of a sequence as a kind of infinite process rather than a fixed value, since a sequence need not reach its limit. Where students accept the difference between a sequence of numbers and its limit, they might read "0.999…" as meaning the sequence rather than its limit.[35]
Some students regard 0.999… as having a fixed value which is less than 1 by an infinitesimal but non-zero amount.
Some students believe that the value of a convergent series is at best an approximation, that .
These ideas are mistaken in the context of the standard real numbers, although some may be valid in other number systems, either invented for their general mathematical utility or as instructive counterexamples to better understand 0.999….

[owheelj]

so does .8999999999999... equal .9?

Of course.

If you incorrectly apply algebraic rules that are meant for real numbers to non-real numbers.

It's all an attempt by the pencil manufacturers to get you to use more pencils. Why write 0.9 when you can write 0.89999999999999999999999999999999?

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

In mathematics, the real numbers may be described informally in several different ways. The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of two; or, a real number can be given by an infinite decimal representation, such as 2.4871773339..., where the digits continue in some way; or, the real numbers may be thought of as points on an infinitely long number line.

I guess going to the best maths university in the world doesn't mean that you actually have any idea what you're talking about.

[KLOBBER]

...your first addition on the far right would still be 3.333recurring+3.333recurring+3.333recurring which does not equal 9 (as you mistakenly are stating). It equals 10....

When I first started reading this thread, I thought it was a joke -- everybody knows that .999 recurring falls eternally short of 1. Then I actually went to Wikipedia, and it says there that a certain group of unnamed individuals were at one point of the OPINION that it was somehow true, without citing any evidence to back that OPINION. I still wasn't convinced.

Then the self-styled math whiz kid from Australia, the land of individuals descended from English reprobates and criminals so abhorrent to civilized society that they had to be manacled and ostracized to a dry, barren, hellish island thousands of miles away, almost convinced me with some pretty fast talking.... Almost.

Then I saw Prowler's post, above, and he is right. 3.333 recurring + 3.333 recurring + 3.333 recurring does not equal 9, as Crocodile Dumdum believes.

The type of mind that would have you believe that .999 recurring is equal to 1 is the same type of mind that would have you believe that an infinite number of steps halfway to a given point reaches that point. However, that is not true, since each and every step in the described system only goes halfway there from the point of the previous step.

Such a mind is inflicted with the pernicious disease known as reductionism, and its theories remain unproven and obviously false. Reductionism is a deficiency, a manifestation of an inability to think in alignment with the fullness of reality, a habit of the unintelligent, whose natural position is a lack of understanding, to attempt to make the world easier to grasp, so that it ceases to frighten him. It is an attempt of the mentally deficient to extrapolate his own deficiency onto reality, and it is a failed attempt at every turn.

Each and every additional digit added to .999 recurring only brings you less than 100% of the remaining distance from 1, never all the way to 1, and this applies to any and all additions of the digit 9, even infinite additions -- each one of the infinite additions brings you less than 100% of the remaining distance, leaving the result eternally short of 1. No matter how many decimal points you bring it to the right, no 9 will ever bring the value all the way to 1, just as the first digit 9 does not bring it all the way to 1, and the second digit 9 does not bring it all the way, nor the third, nor the fourth, and so on. Although each one admittedly brings it closer than the previous, it is mathematically unsound to believe that any of those 9's down the line will be any different from its predecessor digit 9's -- no digit 9 or group of digit 9's anywhere in the string .999 recurring brings you all the way there any more than any of its predecessors. Such a digit 9 or group of digit 9's simply does not exist in reality.

That is why we have the digit 1. It is a different number than .999 recurring, no matter what unnamed individuals' OPINIONS are cited on Wikipedia (which is edited by laymen, BTW), and no matter what half-matured, half-baked descendant of uncontrollable criminals posts a similar OPINION after having been so weak-minded as to be easily brainwashed into believing it.

My work here is done.

[Snorri1234]

lol, double troll.

[owheelj]

And just a quick correction, because I keep seeing this quoted; 1/9 does not equal 0.999... It equals 0.111...

[TheProwler]

so does .8999999999999... equal .9?

Of course.

If you incorrectly apply algebraic rules that are meant for real numbers to non-real numbers.

uh in what way is .8999... not a real number

Well, it is....but the amount of precision is infinite....it is a non-real amount of precision. It is "infinity" that is the non-real number. I admit to this mistake. I'm not sure of the proper terms. Like I said, it has been a long time since I've been studying this kind of stuff. But my understanding is clear.

Nobody has addressed the simple fact that our system of recording numbers is flawed (without the use of fractions). Can't you see that 0.333recurring is not as accurate as 1/3? It encourages mistakes like 3 * 0.333recurring equals 0.999recurring.

Someone posed a question about going halfway from point A to point B, with every step. How long would it take to get to point B? How many steps? An infinite number? How long would take? An infinite amount of time?

Why did nobody answer?

This is similar to 0.999recurring equaling 1. It is almost there. Almost. Another trillion 9's and we're almost there. Almost. You will never get there.

Rules of Algebra do not apply when posed with an imprecise number.

This is like the "When the universe ends, what's on the other side?" type of conversation. People can't really grasp infinity. The difference between 1 and 0.999recurring is infinitely small. But it is a non-zero number.

[sully800]

0.33333recurring = 1/3
0.99999recurring = 1/9

I think I might have spotted a mistake there sully dear chap.

LOL

Sorry for the type everyone, ruined a post and a few people's minds it appears.

Corrected to say 0.9999recurring = 3/3 = 1

[owheelj]

Then I saw Prowler's post, above, and he is right. 3.333 recurring + 3.333 recurring + 3.333 recurring does not equal 9, as Crocodile Dumdum believes.

I have never claimed that 3.333... +3.333... + 3.333 = 9 I clearly claimed that 3+3+3=9. 3=/= 3.333... I'm not sure where this confusion comes from.

You are right that wikipedia is edited by laymen, but the 50 or so text books it refers to are not. Find me any mathematical source that claims that 0.999... does not equal 1 and I will consider your opinion to be meaningful.

[sully800]

0.33333recurring = 1/3
0.99999recurring = 1/9

I think I might have spotted a mistake there sully dear chap.

LOL

Sorry for the typo everyone, ruined a post and a few people's minds it appears.

Corrected to say 0.9999recurring = 3/3 = 1

For Prowler and Klobber: How much smaller is 0.99999recurring than 1.0? You both seem to agree that it is smaller. So by how much?

[owheelj]

The type of mind that would have you believe that .999 recurring is equal to 1 is the same type of mind that would have you believe that an infinite number of steps halfway to a given point reaches that point. However, that is not true, since each and every step in the described system only goes halfway there from the point of the previous step.

What a great analogy.

http://en.wikipedia.org/wiki/Zeno's_par ... oxes_today

Calculus removes this paradox. It was one of the first things you learn about when you start learning calculus.

[TheProwler]

...your first addition on the far right would still be 3.333recurring+3.333recurring+3.333recurring which does not equal 9 (as you mistakenly are stating). It equals 10....

When I first started reading this thread, I thought it was a joke -- everybody knows that .999 recurring falls eternally short of 1. Then I actually went to Wikipedia, and it says there that a certain group of unnamed individuals were at one point of the OPINION that it was somehows true, without citing any evidence to back that OPINION. I still wasn't convinced.

Then the self-styled math whiz kid from Australia, the land of individuals descended from English criminals so repulsive to society that they had to be deported to a dry, barren, hellish island thousands of miles away, almost convinced me with some pretty fast talking.... Almost.

Then I saw Prowler's post, above, and he is right. 3.333 recurring + 3.333 recurring + 3.333 recurring does not equal 9, as Crocodile Dumdum believes.

The type of mind that would have you believe that .999 recurring is equal to 1 is the same type of mind that would have you believe that an infinite number of steps halfway to a given point reaches that point. However, that is not true, since each and every step in the described system only goes halfway there from the point of the previous step.

Such a mind is inflicted with the pernicious disease known as reductionism, and its theories remain unproven and obviously false. Reductionism is a deficiency, a manifestation of an inability to think in alignment with the fullness of reality, a habit of the unintelligent, whose natural position is a lack of understanding, to attempt to make the world easier to grasp, so that it ceases to frighten him. It is an attempt of the mentally deficient to extrapolate his own deficiency onto reality, and it is a failed attempt at every turn.

Each and every additional digit added to .999 recurring only brings you less than 100% of the remaining distance from 1, never all the way to 1, and this applies to any and all additions of the digit 9, even infinite additions -- each one of the infinite additions brings you less than 100% of the remaining distance, leaving the result eternally short of 1. No matter how many decimal points you bring it to the right, no 9 will ever bring the value all the way to 1, just as the first digit 9 does not bring it all the way to 1, and the second digit 9 does not bring it all the way, nor the third, nor the fourth, and so on. Although each one admittedly brings it closer than the previous, it is mathematically unsound to believe that any of those 9's down the line will be any different from its predecessor digit 9's -- no digit 9 or group of digit 9's anywhere in the string .999 recurring brings you all the way there any more than any of its predecessors. Such a digit 9 or group of digit 9's simply does not exist in reality.

That is why we have the digit 1. It is a different number than .999 recurring, no matter what unnamed individuals' OPINIONS are cited on Wikipedia (which is edited by laymen, BTW), and no matter what half-matured, half-baked descendant of uncontrollable criminals posts a similar OPINION after having been so weak-minded as to be easily brainwashed into believing it.

My work here is done.

Hold the phone!!!! Wikipedia is edited by laymen?

Is it kinda a first-come, first serve thing? Hahaha!

They forgot to carry the 1!!

[Timminz]

For Prowler and Klobber: How much smaller is 0.99999recurring than 1.0? You both seem to agree that it is smaller. So by how much?

Think of it as
10x - x = 9.00000...0000001

He managed to find the end of an infinite string.

[TheProwler]

Then I saw Prowler's post, above, and he is right. 3.333 recurring + 3.333 recurring + 3.333 recurring does not equal 9, as Crocodile Dumdum believes.

I have never claimed that 3.333... +3.333... + 3.333 = 9 I clearly claimed that 3+3+3=9. 3=/= 3.333... I'm not sure where this confusion comes from.

You should look at the example I provided until you understand it as KLOBBER did.

[owheelj]

This is similar to 0.999recurring equaling 1. It is almost there. Almost. Another trillion 9's and we're almost there. Almost. You will never get there.

Some students regard 0.999… as having a fixed value which is less than 1 by an infinitesimal but non-zero amount.

These ideas are mistaken in the context of the standard real numbers, although some may be valid in other number systems, either invented for their general mathematical utility or as instructive counterexamples to better understand 0.999…

[TheProwler]

For Prowler and Klobber: How much smaller is 0.99999recurring than 1.0? You both seem to agree that it is smaller. So by how much?

And infinitely small, non-zero, number. You should read the thread.

[owheelj]

Then I saw Prowler's post, above, and he is right. 3.333 recurring + 3.333 recurring + 3.333 recurring does not equal 9, as Crocodile Dumdum believes.

I have never claimed that 3.333... +3.333... + 3.333 = 9 I clearly claimed that 3+3+3=9. 3=/= 3.333... I'm not sure where this confusion comes from.

You should look at the example I provided until you understand it as KLOBBER did.

Xeno's paradox? You should really learn basic calculus.

[KLOBBER]

...How much smaller is 0.99999recurring than 1.0...?

Your question is akin the the child's question, "Daddy, how big is infinity?" Your question, similar to the child's question that includes infinity, includes an infinite string. The standard answer to the child's question is, "Bigger than you can comprehend."

Still, here is the answer, and it is similar to the standard answer to the child's question, above: The difference is smaller than you can comprehend, but, most importantly, it is greater than 0. It is interesting to note that, just as the child's question asserts, by asking how big, that infinity is indeed "big," so your question asserts, by asking how much smaller, that .999 recurring is indeed "smaller than 1." Congratulations -- it seems that you understand!

And no, just because I know how tricksy is the reductionist mind, infinitely small does not equal zero. Any small positive number is, by definition, greater than zero, just as any small negative number is, by definition, less than zero, even infinitely small positive and infinitely small negative numbers.

I couldn't resist answering this question, but I'm not going to get pulled any further into this conversation, which is infested by brainwashed, nonsense reductionist parrots.

As I already said, my work here is done.

[TheProwler]

For Prowler and Klobber: How much smaller is 0.99999recurring than 1.0? You both seem to agree that it is smaller. So by how much?

Think of it as
10x - x = 9.00000...0000001

He managed to find the end of an infinite string.

Haha, I said "Think of it as" to help you understand. I guess it wasn't much help.

[InkL0sed]

For Prowler and Klobber: How much smaller is 0.99999recurring than 1.0? You both seem to agree that it is smaller. So by how much?

And infinitely small, non-zero, number. You should read the thread.

That number is impossible. Infinitely small = 0

[TheProwler]

This is similar to 0.999recurring equaling 1. It is almost there. Almost. Another trillion 9's and we're almost there. Almost. You will never get there.

Some students regard 0.999… as having a fixed value which is less than 1 by an infinitesimal but non-zero amount.

These ideas are mistaken in the context of the standard real numbers, although some may be valid in other number systems, either invented for their general mathematical utility or as instructive counterexamples to better understand 0.999…

Dude, enough with the wiki. It doesn't prove a thing. It proves that someone agrees with you.

On this topic, like many others, a very small percentage of people will be able to really understand it. It doesn't come down to a vote count.

[Snorri1234]

Love this thread. Absolutely fucking love it.