MrDudeMan
Lifer
- Jan 15, 2001
- 15,069
- 94
- 91
that is flawed. it is impossible for something to equal something else if it isnt EXACTLY THE SAME. 291FSB is not the same as 290.999999FSB. it simply is not the same. i can see both sides of this arguement, and proofs like this are just as stupid as "can god make a rock he cant lift?" its such a stupid fallacy that it kills the arguement. find a real reason that .99999=1 and then prove it. it will never, ever reach 1.
I hate to get involved in threads of fact vs. stupidity... but which of the above steps do you disagree with? 1/3 = .33333...? You can evaluate that by hand. 1/3 + 1/3 + 1/3 = 1? Go back to elementary school, again, you can evaluate it by hand. Combining the two, you get .3~ + .3~ + .3~ = 1. From there, you get .9~ = 1. What's the problem?
I'm not arguing against .999... equaling 1, but I've always hated the 1/3 argument. It basically says: "Assume our hypothesis is true. Under this assumption, our hypothesis is true." One could argue against it by saying that .333... is the best representation for 1/3 that is available in base 10 but that it isn't truly equal to 1/3 (since there is always a remainder). If you want to PROVE it, you have to use calculus, not simple arithmetic. Just my two cents...
Why do you have to use calc to prove something? Algebra / arithmetic work fine. Use the simplest tool to get the job done. None of the steps in that proof are invalid.
Let me guess... you don't know calc, and then when someone uses calc to prove it (do you consider infinite series/sequences/sums to be calc? they're usually taught in Calc I or II...) you'll ask them to explain in a way you can follow?
YES OF COURSE IT DOES!
Funny I was just reading one of these threads a few days ago then in calc we were shown they were equal with an infinite series. For anyone who doesn't believe it, the infinite series proof just owned them.
Funny I was just reading one of these threads a few days ago then in calc we were shown they were equal with an infinite series. For anyone who doesn't believe it, the infinite series proof just owned them.
False!
I've taken up through the fifth quarter of college-level calculus. I'm not saying that you can't prove things with algebra. I'm saying that .999... = 1 for the same reasons that calculus works (basically, limits and a usable concept of infinity).I'm also saying that using 1/3 = .333... to prove that .999... = 1 seems like circular logic. The people who don't accept that .999... means there really are an infinite number of 9's after the decimal point won't accept that .333... means there are an infinite number of 3's after the decimal point.
Originally posted by: EpsiIon
False!
I'm also saying that using 1/3 = .333... to prove that .999... = 1 seems like circular logic. The people who don't accept that .999... means there really are an infinite number of 9's after the decimal point won't accept that .333... means there are an infinite number of 3's after the decimal point.
They should... as I said, you can deduce it by hand. After a couple of digits you should realize the pattern.
I'm sorry I caught this thread so late...and that it just keeps going. However, I just wanted to say that, in the grand scheme of things, 2+2=5, for large values of two, that is.........................................
j'son
j'son
Originally posted by: CTho9305
Originally posted by: EpsiIon
False!
I'm also saying that using 1/3 = .333... to prove that .999... = 1 seems like circular logic. The people who don't accept that .999... means there really are an infinite number of 9's after the decimal point won't accept that .333... means there are an infinite number of 3's after the decimal point.
They should... as I said, you can deduce it by hand. After a couple of digits you should realize the pattern.
No, no, no. It's not that they don't see the pattern. It's that they can't comprehend infinity being used in a finite way.
Here was what originally kept me from understanding: I saw infinity not as a quantity but as an ever-increasing number. So, when I thought about an infinite number of 9's, I thought they were being appended eternally. Something that's constantly growing does not have a finite value and so cannot be constantly equal to anything but itself. When I realized that the infinite number of 9's after the decimal point is very similar to an infinite number of subdivisions in a Riemann sum, the picture became a bit more clear.
As a side note, I'm willing to be that a lot of people can't understand the concept of infinities of different sizes, too.
SagaLore
Elite Member
- Dec 18, 2001
- 24,036
- 21
- 81
.333..., .666..., .999... do not exist. Repeating numbers are an imaginary construct to get by with the flaw of the decimal system. Only whole integers and ratios can represent accurate values when dealing with partials.
I would conclude that even .3333... does not equal 1/3.
0.999999999.... is NOT equal to 1 !!! If 0.99999.... was equal to 1, it would be written as one. Is 2.99999999... equal to 3? Is 99.99999999... equal to 100? NO !!! 0.99999... may be about as close as you can get to being 1, without being 1, but, it is not equal to 1.
How old are you?
I'm 14.99999999.
Oh, so you're 15?
No, I turn 15 in 1 yoctosecond.
lol, get it?
.333333... is not 1/3 of 10 , as some people have already said.
.333333... will never be 1/3 of 10 because even though you
keep adding threes, you only get a little closer to being 1/3,
.33333... will never be 1/3 of 10, even with an infinite amount of 3's
How old are you?
I'm 14.99999999.
Oh, so you're 15?
No, I turn 15 in 1 yoctosecond.
lol, get it?
.333333... is not 1/3 of 10 , as some people have already said.
.333333... will never be 1/3 of 10 because even though you
keep adding threes, you only get a little closer to being 1/3,
.33333... will never be 1/3 of 10, even with an infinite amount of 3's
Legendary
Diamond Member
- Jan 22, 2002
- 7,019
- 1
- 0
http://www.blizzard.com/press/040401.shtml
If Blizzard says so, I believe it.
Edit: http://aah.ryan-usa.com/node30.html
Scroll to the middle of that page and read the series proof - more proof than you should ever need.
If Blizzard says so, I believe it.
Edit: http://aah.ryan-usa.com/node30.html
Scroll to the middle of that page and read the series proof - more proof than you should ever need.
You wanna know why Blizzard, and everyone else is wrong? It's because 9x is actually 8.9991, if x=.99999 -as they state. I'm in grade 9 and I figured this out. C'mon, end it already.
As for that second link, that guy himself states that .99 (with the bar overhead) does not equal 1. So there.
As for that second link, that guy himself states that .99 (with the bar overhead) does not equal 1. So there.
I'm not sure I'd call it a "flaw." Furthermore, the concept that "only whole integers and ratios can represent accurate values when dealing with partials" died around the time of Pythagoras. If you disagree, then give me the precise value of the diagonal of a square with sides of length 1. I'll be content with sqrt(2). But, that cannot be represented as a ratio. (and the proof is fairly simple if you need it)
Most of the people trying to prove that .9999... != one make statements that are not true in the real number system. They are, however, true in the hyperreal number system.
The concept of the number .999... as a seperate entity from 1 is simply wrong in the real number system. False. Untrue. By definition, it is the same. However, the hyperreal system, which allows us to rigoruously prove the calculus as practiced by Leibniz and Newton, allows for .999... to be different than one... in the hyperreal system, every real number has an infinite number of "halo" 's around it, numbers that are infinitesimally close, but not quite.
See here, here, and most importantly, a free calculus textbook that uses the infinitesimal approach to calculus instead of the standard limit approach.
It is interesting to see that we can actually push the real number system to the point of failure, simply by asking one straightforward question:
"What is the smallest positive number?"
Specifically: if we define the variable d as the answer to this question, then the real number system fails to provide a well-defined numeric value for d.
We can cause the real number system to fail in other ways by asking other questions, such as: "What is 1 divided by 0?", or "What is the square root of -1?". (The real number system is perhaps not as robust as you might have assumed.)
Each time another failure occurs in the real number system, it triggers the creation of another branch of mathematics. The failure to find a real value for d triggers the creation of the hyperreal number system, which is an extension to the real number system that allows us to give a well-defined value to d by creating the concept of infinitesimal numbers that are distinct from 0.
The concept of the number .999... as a seperate entity from 1 is simply wrong in the real number system. False. Untrue. By definition, it is the same. However, the hyperreal system, which allows us to rigoruously prove the calculus as practiced by Leibniz and Newton, allows for .999... to be different than one... in the hyperreal system, every real number has an infinite number of "halo" 's around it, numbers that are infinitesimally close, but not quite.
See here, here, and most importantly, a free calculus textbook that uses the infinitesimal approach to calculus instead of the standard limit approach.
It is interesting to see that we can actually push the real number system to the point of failure, simply by asking one straightforward question:
"What is the smallest positive number?"
Specifically: if we define the variable d as the answer to this question, then the real number system fails to provide a well-defined numeric value for d.
We can cause the real number system to fail in other ways by asking other questions, such as: "What is 1 divided by 0?", or "What is the square root of -1?". (The real number system is perhaps not as robust as you might have assumed.)
Each time another failure occurs in the real number system, it triggers the creation of another branch of mathematics. The failure to find a real value for d triggers the creation of the hyperreal number system, which is an extension to the real number system that allows us to give a well-defined value to d by creating the concept of infinitesimal numbers that are distinct from 0.
Ok, scroll down to the bottom of the page at the website given earlier. You should see a little something called a geometric series. Look at the proof. You can't argue with that. If your argument is with the series itself, look up a proof; it's valid.
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