What is .99 repeating as a fraction?
List of common misconceptions
"Contrary to a widespread perception, the real number 0.999...
where the decimal point is followed by an infinite sequence of nines
is exactly equal to 1.[283]
They are two different ways of writing the same real number."
The formula of an infinite geometric series IS the proof.
Most can not grasp that an infinite number of something, in this case .9 + .09 + .009 + .0009 + .00009 + .000009 ... can have a finite number as a sum.
But it does.
I agree that those who say .999... does not equal 1, that the two are not the same must then prove the infinite geometric series formula of a*r/1-r is false.
Quote: DocWhich are equal.
If 1.999... and 2 are equal, what value do they hold. Does 1.999... have the value of 2, or does 2 have the value of 1.999... ?
I have an equation that shows 1.999... has a value of 1.999... and 2 has a value of 2.
Yes, exactly.Quote: JyBrd0403Does 1.999... have the value of 2, or does 2 have the value of 1.999... ?
a - b = c
If a and b are the same number then c must equal 0. Correct?
If a and b are different numbers then c must ba a non-zero number. Agree?
Now substitute these two numbers in:
2 - 1.999... = c
where 1.999... means that there are an infinite number of 9's following the last digit.
Question then is what is the value of c?
If you believe that 2 and 1.999... are different numbers then c is non-zero. What then is this non-zero number? I could always define 1.999... to as many decimal places as I want to always make sure that c would always come out to be zero regardless of how many decimal places you have on your calculator or computer. Therefore you have to accept the fact that 2 and 1.999.... are mathematically the same number.
Interestingly this is also how you can define an infinitesmal quantity in calculus.
We have seen in the past that JyBrd0403 claims the answer is "a number greater than zero" but refuses to say what that number is or how he would represent it. It appears to be a case of refusing to accept defeat in the face of overwhelming evidence, just by declaring that defeat is impossible.Quote: paisielloQuestion then is what is the value of c?
I asked quite a few of my co-workers this question and 3 out of 4 say the 2 are not the same value.Quote: paisiellowhere 1.999... means that there are an infinite number of 9's following the last digit.
If you believe that 2 and 1.999... are different numbers
The reason given by those who said they are different is almost the same.
2 is a finite number
1.999... is an number with an infinite number of 9s.
So, they can't be equal because one is finite and the other is infinite.
After showing why they are equal and how they do represent the same value, still over 50% disagreed that they are the same because a finite number can never equal an infinite number.
Even with proof, many will still disagree for one reason or another.
(It's ok, they work in the business department)...
Isn't 2 an infinite number as well?
2.000... ???
After all, it's just a matter of representing the same number different ways, right?
Me too.Quote: QuadDeucesI swore to myself I wouldn't post on this thread...
Isn't 2 an infinite number as well?
2.000... ???
After all, it's just a matter of representing the same number different ways, right?
Is not 0 the absence of a number in decimal form?
.000... = 0/10 + 0/10^2 + 0/10^3 + 0/10^4 etc.
So there really are no numbers there.
But 0 is a number otherwise. Oh oh.
Prooving that 0.999... = 0.999... is not proof that 0.999... does not equal 1.
Quote: TriplellI'm still waiting on proof that 0.999... doesn't equal 1.
Prooving that 0.999... = 0.999... is not proof that 0.999... does not equal 1.
So, I did prove that .999... = .999... triplell? I'll take that as a minor victory. You've been saying for 40 pages that .999... is 1. Now, apparently it is also .999... and has 2 different values .999... and also 1. Is this correct?
Quote: JyBrd0403Now, apparently it is also .999... and has 2 different values .999... and also 1. Is this correct?
Almost. Except, it is actually the same value, not "two different values". 0.999..., 1, 1.000... 4/4, etc. all have the same value (defined as the first natural number, or the unity in the field of integers if you prefer).
1/3 = .333... in base 10 = .3 in base 9.
.333... x 3 in base 10 equals .999...
.3 x 3 in base 9 equals 1.0, not some number less than 1.0
Stop confusing numbers with numerical representation.
1/3 * 3 = 1. Even an idiot like me can see that. I know, right?
Quote: weaselmanall have the same value (defined as the first natural number, or the unity in the field of integers if you prefer).
I don't know what this means (sounds like nonsense, though)Is .999... the value of 1, or is 1 the value of .999... since they both share the same value, which is it? I assume it means .999... has the value of 1, and 1 has the value of 1 and not .999... , correct?
Also, what is the value of .333... , .666... etc.? Since, repeating decimals don't have a value of their own, now.
I still have an equation that shows .333...= .333... .666... = .666... .999... = .999... and 1=1.
Quote:what is the value of .333...
1/3
Quote:.666...
2/3
Quote:etc.?
You mean .999...?
3/3
In the decimal system, .333... is the best possible representation of 1/3.
Again, if you would chop off a finger (might I suggest the finger that you use to click the post button), .3 in base nine perfectly represents 1/3, and .3 x 3 = 1.0 (base 9) not some value other than 1.0.
Why don't you guys just list your math degrees and the one with the most advanced degree, from the most prestigious institution, wins!
Quote: QuadDeucesStop confusing numbers with numerical representation.
Quote: QuadDeucesStop confusing numbers with numerical representation.
Quote: QuadDeucesYou also see a whole divided into three equal parts with no numerical representation at all. One of those parts is the value of 1/3, .333... (base 10), and .3 (base 9).
So what? What are you talking about. I'm pretty sure this thread is about base 10.
Hey, what's .333...'s number value anyway? I have it as being .333... Weaselman, says it doesn't have a value at all.
Oh wait, you just said it's value is .333... , so we agree. Weaselman is wrong.
I can give you a numerical representation for it, but that's a different argument. All you have to do is say .999... is not equal to 1. And, I'll give you that number that's not represented by .333... x 3. Once you understand .999... is not equal to 1. You'll understand that number as well.
Quote:I guarantee you it's a number > 0. You see those white lines dividing the whole. That's the part that's not represented.
Good night.
Quote: JyBrd0403I guarantee you it's a number > 0. You see those white lines dividing the whole. That's the part that's not represented.
I can give you a numerical representation for it, but that's a different argument. All you have to do is say .999... is not equal to 1. And, I'll give you that number that's not represented by .333... x 3. Once you understand .999... is not equal to 1. You'll understand that number as well.
.999... does not equal .999...
however,
.999... does equal 1.
Right?
Quote: JyBrd0403So, where were we? Oh yes.
.999... does not equal .999...
however,
.999... does equal 1.
Right?
you're close
Quote: JyBrd0403So, where were we? Oh yes.
.999... does not equal .999...
however,
.999... does equal 1.
Right?
Quote: Triplellyou're close
Oh, yeah yeah yeah.
.999... does not have the value of .999...
instead,
.999... has the value of 1.
Better?
I'm just curious, if that's the case, what's the value of .333... or .666... ?
Quote: JyBrd0403Oh, yeah yeah yeah.
.999... does not have the value of .999...
instead,
.999... has the value of 1.
Better?
I'm just curious, if that's the case, what's the value of .333... or .666... ?
Quote: DocConsidering the recent posts, I'm getting the idea that JyBrd doesn't recognize when he is being mocked.
No, doc, I'm just used to it.
All right, enough game play, Doc. You wanted to know what the representation for 1 - .999... is. My answer is .000...
As with all repeating decimals, the ... at the end shows that there is an active calculation being done. The number does not come to an end. The number 0 doesn't have the ... at the end of it, which tells us there is no active calculation being done to this number. There are no repeating 0's.
So, my representation for that number would be .000... as opposed to just plain 0.
Mock away.
Which are, of course, equal.Quote: JyBrd0403So, my representation for that number would be .000... as opposed to just plain 0.
Quote: DocWhich are, of course, equal.
What's the value of .333... and .666... ?
If .333... has the value of .333... and .666... has the value of .666... , then .999... has the value of .999... and .000... has the value of .000...
Quote: DocWe have seen in the past that JyBrd0403 claims the answer is "a number greater than zero" but refuses to say what that number is or how he would represent it. It appears to be a case of refusing to accept defeat in the face of overwhelming evidence, just by declaring that defeat is impossible.
Are you refusing to say what the value of .333... and .666... are, doc?
By the way, I threw .000... into the top of my equation, it came out .000... on the bottom of the equation also.
i guess that means by the same logic that because .000... = .000..., then .000... != 0 somehow
thanks for showing us why your proof relies on a logical falacy, it will save us the time arguing that out.
it was proven twice already:
A: 1/3 = .333...
3*1/3 = 3*.333...
1=.999...
B: 1 - .999... = 0.000... = 0
(you can't say 1 - .999... = .000...1 because the string of 0's never ends by definition of infinity, thus the statement "with a 1 at the end" is self defeating as there is no end of an infinate string)
but i have a feeling this is like arguing with a conspiracy theorist now, where the more logic and evidence point to the contrary, the stronger rather than weaker will the theorist fall upon his beliefs, so this thread should really just die at this point unless he can come up with two really compelling arguements to counter our proofs AND offer a new proof not based on a logical falacy beacuse if he can't and still chooses to believe .999... != 1, then it is because he wants to, and no amount of reasoning can counter someone who wants to believe something that isn't true (betting system forum proves that pretty well)
Quote: GamerMan....so this thread should really just die at this point.....
It was dead for a week before you posted to it.
Mine did. Every time one butt cheek got numb, I shifted to the other one.Quote: WizardJust out of curiosity, did anybody's position change over the course of this thread?
That didn't stop .9999.... from being 1, though.
And yes, this is the first time in a year that I felt the need to post here. Speaks volumes about me, I know.
Quote: TriplellWhat was your position Wiz?
My position is that 0.999...=1.
Here is what I find to be a more interesting question. A random number is chosen from a uniform distribution between 3 and 4. What is the probability it is NOT pi? If your answer is 1, is that the same as a hard 1?
Well, let's see...Quote: WizardJust out of curiosity, did anybody's position change over the course of this thread?
This thread started on February 2nd, 2012 at 11:23:28 AM
You posted the above question on March 27th, 2012 at 7:32:37 AM
I calculate an interval of 53 days, 20 hours, 10 minutes, 9 seconds.
That's 1,292.16916666666.... hours.
The Earth orbits the sun at a speed of about 107,000 km/h (source: Wikipedia).
Multiplied, that comes to 138,262,100.8333333333333... km.
So, to answer your question, my position changed about 138 million kilometers. I say "about" because Earth's orbit is round, so we can't really use a linear measurment to come up with the distance from one end to the other end of that arc segment, and I was never any good at that type of math. So "About" works for me.
Oh.
You mean my position on Repeating Decimals?
Nope. No change.
0.999999.... = 1
Quote: DJTeddyBearSo, to answer your question, my position changed about 138 million kilometers. I say "about" because Earth's orbit is round, so we can't really use a linear measurment to come up with the distance from one end to the other end of that arc segment, and I was never any good at that type of math. So "About" works for me.
You've aslo failed to take into account the Sun's movement around the center of the Galaxy (dragging the Earth along with it), and the Galaxy's movements, not to mention the expanding Universe :)
But then these are the types of comments that get me blocked...
Damn!Quote: pob14Mine did. Every time one butt cheek got numb, I shifted to the other one.
That didn't stop .9999.... from being 1, though.
And yes, this is the first time in a year that I felt the need to post here. Speaks volumes about me, I know.
And I thought *I* was gonna win the "Best Wise Ass response" award.
Congrats. And welcome!
I thought about it, but figured I was being enough of a smart ass. And that was before I saw pob14's response.Quote: NareedYou've aslo failed to take into account the Sun's movement around the center of the Galaxy (dragging the Earth along with it), and the Galaxy's movements, not to mention the expanding Universe :)
Nah...Quote: NareedBut then these are the types of comments that get me blocked...
Thanks. And it generally takes a lot to beat me in a WiseAss contest.Quote: DJTeddyBearDamn!
And I thought *I* was gonna win the "Best Wise Ass response" award.
Congrats. And welcome!
Now at 2 entirely content-free posts and counting . . . . :-)
Quote: WizardIf your answer is 1, is that the same as a hard 1?
Are you implying there is more than one number with the value 1? :)
Quote: WizardMy position is that 0.999...=1.
Here is what I find to be a more interesting question. A random number is chosen from a uniform distribution between 3 and 4. What is the probability it is NOT pi? If your answer is 1, is that the same as a hard 1?
Probability of the number NOT being Pi is 99.999...%
Here's what's more interesting. The probability of the number being Pi is .000...% . If you were to just say 0%, that would mean Pi doesn't exist. Pi is an irrational little number, but it DOES exist.
