.9999999999999 = 1

[vfpreacher111]

@ journeymen

LMAO !!!!

Lets use liquid then. If a container holds EXACTLY .999999 oz.
and you put in EXACTLY 1 oz. it will spill over..... fuzzy rounding up or down math or not.



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[gauSSian]

Originally Posted by journeymen

Fixed

thank you.

Originally Posted by TheWacoKid

This doesn't make and sense at all...

indeed it does not.

Originally Posted by georgesoul

can I change sides? they've convinced me, .999...=1.

yes.

[Waco]

Originally Posted by vfpreacher

@ journeymen

LMAO !!!!

Lets use liquid then. If a container holds EXACTLY .999999 oz.
and you put in EXACTLY 1 oz. it will spill over..... fuzzy rounding up or down math or not.

We aren't talking about .999999. We're talking about .999...

The two numbers are infinitely different. There's no rounding involved in the equation .999... = 1. It's exact.

Here's an exercise for those that don't believe it's correct. Name a SINGLE number between .999... and 1.

[gauSSian]

Originally Posted by vfpreacher

... .999999 oz. ...

.999999 ≠ 0.999...

a finite number is not infinite. do you see how the two differ. one goes on and on forever, and the other can be quantified with a real finite number.

[OldVetteFan]

0.999... = 1 is a mathematical identity, and is completely acceptable to any professional mathemetician.

From Wikkipedia ...

In mathematics, the recurring decimal 0.999… , which is also written as or , denotes a real number equal to 1. In other words, "0.999…" represents the same number as the symbol "1". The equality has long been accepted by professional mathematicians and taught in textbooks. Various proofs of this identity have been formulated with varying rigour, preferred development of the real numbers, background assumptions, historical context, and target audience.

In the last few decades, researchers of mathematics education have studied the reception of this equality among students. A great many question or reject the equality, at least initially. Many are swayed by textbooks, teachers and arithmetic reasoning as below to accept that the two are equal. However, they are often uneasy enough that they offer further justification. 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 unique decimal expansion must correspond to a unique number, that nonzero infinitesimal quantities should exist, or that the expansion of 0.999… eventually terminates.

The non-uniqueness of such expansions is not limited to the decimal system. The same phenomenon occurs in integer bases other than 10, and mathematicians have also quantified the ways of writing 1 in non-integer bases. Nor is this phenomenon unique to 1: every non-zero, terminating decimal has a twin with trailing 9s. For reasons of simplicity, the terminating decimal is almost always the preferred representation, further contributing to the misconception that it is the only representation. In fact, once infinite expansions are allowed, all positional numeral systems contain an infinity of ambiguous numbers. For example, 28.3287 is the same number as 28.3286999…, 28.3287000, or many other representations. These various identities have been applied to better understand patterns in the decimal expansions of fractions and the structure of a simple fractal, the Cantor set. They also occur in a classic investigation of the infinitude of the entire set of real numbers.

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.[1]
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".[2]
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.[3]
Some students regard 0.999… as having a fixed value which is less than 1 by an infinitely small amount.
Some students believe that the value of a convergent series is an approximation, not the actual value.
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….

Many of these explanations were found by professor David Tall, who has studied characteristics of teaching and cognition that lead to some of the misunderstandings he has encountered in his college students. Interviewing his students to determine why the vast majority initially rejected the equality, he found that "students continued to conceive of 0.999… as a sequence of numbers getting closer and closer to 1 and not a fixed value, because 'you haven’t specified how many places there are' or 'it is the nearest possible decimal below 1'".[4]

Of the elementary proofs, multiplying 0.333… = 1⁄3 by 3 is apparently a successful strategy for convincing reluctant students that 0.999… = 1. Still, when confronted with the conflict between their belief of the first equation and their disbelief of the second, some students either begin to disbelieve the first equation or simply become frustrated.[5] Nor are more sophisticated methods foolproof: students who are fully capable of applying rigorous definitions may still fall back on intuitive images when they are surprised by a result in advanced mathematics, including 0.999…. For example, one real analysis student was able to prove that 0.333… = 1⁄3 using a supremum definition, but then insisted that 0.999… < 1 based on her earlier understanding of long division.[6] Others still are able to prove that 1⁄3 = 0.333…, but, upon being confronted by the fractional proof, insist that "logic" supersedes the mathematical calculations.

You can read more here ...

http://en.wikipedia.org/wiki/0.999...

Again, the original poster didn't make his title correct, as he left off the ellipse. Therefore, his assertion is incorrect.

.9999999999999 = 1 is false. There's no ellipse. He should have made it

0.9999999999999... = 1 and that would have been correct.

Feel free to continue to argue about this, but it's similar to midieval monks arguing about how many angels can dance on the head of a pin.

Steven

[gauSSian]

Originally Posted by VetteUSA93

no, what i'm effectively stating is that .9999999999... isn't 3/3.

actually it is...

0.999... = 9/9 = 3/3 = 1.

in binary, 0.111... = 1 also.

in trinary 0.222... = 1

in octal 0.777... = 1

in hexadecimal 0.FFF... = 1

see a pattern?

[gauSSian]

Originally Posted by OldVetteFan

...Feel free to continue to argue about this, but it's similar to midieval monks arguing about how many angels can dance on the head of a pin.

Steven

the idiocy of arguing over a proven mathematical identity has made me laugh at myself.

[vfpreacher111]

@ TheWacoKid

That's not what the original post says. It says ".9999999999999 = 1" not 9999.... infinity, equals 1. At some point it would be to small to measure, so case could be made for .999999.....> equaling 1. The same case could be made for it never quit equalling one.



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[gauSSian]

another way to state it...

[Waco]

Originally Posted by vfpreacher

@ TheWacoKid

That's not what the original post says. It says ".9999999999999 = 1" not 9999.... infinity, equals 1.

Nobody is arguing that .9999999999999 = 1.

Originally Posted by vfpreacher

At some point it would be to small to measure, so case could be made for .999999.....> equaling 1. The same case could be made for it never quit equalling one.

That's not why we say it equals one.

[OldVetteFan]

Originally Posted by vfpreacher

@ TheWacoKid

That's not what the original post says. It says ".9999999999999 = 1" not 9999.... infinity, equals 1. At some point it would be to small to measure, so case could be made for .999999.....> equaling 1. The same case could be made for it never quit equalling one.

You're right, VFP, and I've pointed it out a couple of times previously.

However, I'm sure that the OP meant 0.999... = 1, and that is apparently the way most people here are taking it. In that case, the identity is correct and true. The OP's mistake is NOT true.

The ellipse ("...") after the nine is math shorthand for an infinite series, and that series converges to one, and is easily proven to be equal to 1. In fact, at least one informal proof has already been posted, and more rigorous proofs can be found by following the Wikkipedia link I posted earlier.

There's no reason that this thread has gone on even this long. The folks that don't believe it can continue to disbelieve it, but their disbelief won't change any currently accepted mathematical theories.

Steven

[Waco]

Originally Posted by OldVetteFan

There's no reason that this thread has gone on even this long. The folks that don't believe it can continue to disbelieve it, but their disbelief won't change any currently accepted mathematical theories.

The people that don't believe it are the same ones that fail the Monty Hall game.

[gauSSian]

Originally Posted by TheWacoKid

The people that don't believe it are the same ones that fail the Monty Hall game.

now you've done it!!!

[Waco]

Originally Posted by gauSSian

now you've done it!!!

I still have the little probability program I wrote to prove people wrong the last time I got in this argument.

[vfpreacher111]

@ OldVetteFan
Ya I saw that after I posted (phone call mid post). Do me a favor and explain it in layman's terms. The way I am reading this is .9...... will continue to increase in size forever drawing closer to the actual number of 1. I see and understand that. How does it make the jump from a never ending shorter distance each time the number increases, to the number 1. I see what you are saying and I read your post.... I still can't get my brain wrapped around the jump to one. And if one is attainable would it be possible for it go to 1.1........ and beyond.



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