irrational numbers like .9 repeating cannot actually exist in a physical sense.
thus, for the sake of reality, .9 repeating equals 1.
thus, for the sake of reality, .9 repeating equals 1.
Last edited by djphetal (2008-02-08 22:54:24)
Neg. If you want to put that forward, you'll need to justify it against several decades of studying the concept of infinity (yes, it's a legitimate study for mathematicians).Skorpy-chan wrote:
No. 0.99 recurring equals 0.99 recurring. It's nearly 1, but not.
Again, 0.999999999999999999999999 does exist. It has its uses also, but becuause of the way maths is constructed, it is technically 1.djphetal wrote:
irrational numbers like .9 repeating cannot actually exist in a physical sense.
thus, for the sake of reality, .9 repeating equals 1.
Last edited by some_random_panda (2008-02-08 22:57:27)
It is not an irrational number.djphetal wrote:
irrational numbers like .9 repeating cannot actually exist in a physical sense.
thus, for the sake reality, .9 repeating equals 1.
It is an expression. A condensed form of notion for an algebraic expansion.
0.999... (condensed algebraic expansion of a summation of a infinite series) is the number 1.
Last edited by topal63 (2008-02-08 23:00:59)
Calculus makes understanding this much easier.
okay you guys win. I thought i was smart but... i don't really actually know what i'm talking about.
That's incorrect. But whatever. I already explained why.tazz. wrote:
Ok....
I aggree with most of what is happening...
Hakie... Your making it more complicated than it has to be....
I AGGREE, 1/3 DOES NOT = 0.3(RECURRING***)
Nothing to the fraction of a third, can be made into an [b]ACCURATE[b] Decimal...
I was meerly pointing out the fact, that common society, accepts that it can be a decimal, although it cannot... and thus, playing around with the fact that 0.9(recurring...) is 1
It's a limit. Read about them.Skorpy-chan wrote:
No. 0.99 recurring equals 0.99 recurring. It's nearly 1, but not.
Last edited by SenorToenails (2008-02-09 21:03:47)
It's funny how people who know nothing about limits, calculus and the concept of infinity argue that 0.999... doesnt equal 1. Guys, 0.9999... equals EXACTLY 1.
Wikipedia has a featured article about 0.99....
From now, I'll reply to every posts made by non-believers by linking to that article. The non-believer will have to show that all the proofs contained in the article are wrong.
Wikipedia has a featured article about 0.99....
Everyone who doesnt believe the concept of 0.99... =1 should read it. It even has a whole section about why non-believers think they are right.Wikipedia wrote:
In mathematics, the recurring decimal 0.999… , 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.
From now, I'll reply to every posts made by non-believers by linking to that article. The non-believer will have to show that all the proofs contained in the article are wrong.
Because that's how it works, instead of refuting what someone says, you're just going to link them to an article.-=raska=- wrote:
It's funny how people who know nothing about limits, calculus and the concept of infinity argue that 0.999... doesnt equal 1. Guys, 0.9999... equals EXACTLY 1.
Wikipedia has a featured article about 0.99....Everyone who doesnt believe the concept of 0.99... =1 should read it. It even has a whole section about why non-believers think they are right.Wikipedia wrote:
In mathematics, the recurring decimal 0.999… , 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.
From now, I'll reply to every posts made by non-believers by linking to that article. The non-believer will have to show that all the proofs contained in the article are wrong.
Wiki this, wiki that.
Fuck deep mathematics, and long drawn out formulas, no matter how many 9's you stick on the end, you're just gonna end up with something close to 1.
Let me ask you this:
If we sit one metre apart, and we cut our distance apart by 9/10ths, and then 9/10ths again and again and again.
Do we ever touch each other?
That's probably why I'll never believe this. Because according to this theory, we would end up touching, no?
Edit: Typo.
Last edited by Hakei (2008-02-09 21:52:21)
/winHakei wrote:
Because that's how it works, instead of refuting what someone says, you're just going to link them to an article.-=raska=- wrote:
It's funny how people who know nothing about limits, calculus and the concept of infinity argue that 0.999... doesnt equal 1. Guys, 0.9999... equals EXACTLY 1.
Wikipedia has a featured article about 0.99....Everyone who doesnt believe the concept of 0.99... =1 should read it. It even has a whole section about why non-believers think they are right.Wikipedia wrote:
In mathematics, the recurring decimal 0.999… , 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.
From now, I'll reply to every posts made by non-believers by linking to that article. The non-believer will have to show that all the proofs contained in the article are wrong.
Wiki this, wiki that.
Fuck deep mathematics, and long drawn out formulas, no matter how many 9's you stick on the end, you're just gonna end up with something close to 1.
Let me ask you this:
If we sit one metre apart, and we cut our distance apart by 9/10ths, and then 9/10ths again and again and again.
Do we ever touch each other?
That's probably why I'll never believe this. Because according to this theory, we would end up touching, no?
Edit: Typo.
I'm going to link them to an article because I'm too lazy to write the proofs again. The article contains a ton a proofs, all you need to do is read them. Oh and read the section that's about the non-believers, it's pretty good. And as I said in me previous post, if you are going to argue with me that 0.999.. is not equal to 1, at least show me that one of the proofs is wrong.Hakei wrote:
Because that's how it works, instead of refuting what someone says, you're just going to link them to an article.
Wiki this, wiki that.
Fuck deep mathematics, and long drawn out formulas, no matter how many 9's you stick on the end, you're just gonna end up with something close to 1.
Let me ask you this:
If we sit one metre apart, and we cut our distance apart by 9/10ths, and then 9/10ths again and again and again.
Do we ever touch each other?
That's probably why I'll never believe this. Because according to this theory, we would end up touching, no?
Edit: Typo.
And to your question, yes we will touch if we do that an infinite amount of times. This is called the concept of limits. But as you know, its impossible for a human to do something an infinite amount of times. And even if we were able to cut our distance by 9/10th a googolplex times, we wouldn't touch.
In 0.999..., there are an infinite amount of 9's. That's why it equals to 1.
Hakei, take calculus courses, it might help. Unless you come back here and tell us that an integral is an approximation...
edit :
noM@rC.ExE wrote:
/win
/fail
/winwiki wrote:
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….
and :
/win.
Last edited by -=raska=- (2008-02-09 22:12:33)
You have no concept of infinity.M@rC.ExE wrote:
/winHakei wrote:
Because that's how it works, instead of refuting what someone says, you're just going to link them to an article.
Wiki this, wiki that.
Fuck deep mathematics, and long drawn out formulas, no matter how many 9's you stick on the end, you're just gonna end up with something close to 1.
This has been explained over and over, and if anyone who does not believe that .999... = 1 read a textbook and the proofs involved, you would understand.
Like I said. Calculus makes understanding this really simple.SenorToenails wrote:
That's incorrect. But whatever. I already explained why.tazz. wrote:
Ok....
I aggree with most of what is happening...
Hakie... Your making it more complicated than it has to be....
I AGGREE, 1/3 DOES NOT = 0.3(RECURRING***)
Nothing to the fraction of a third, can be made into an [b]ACCURATE[b] Decimal...
I was meerly pointing out the fact, that common society, accepts that it can be a decimal, although it cannot... and thus, playing around with the fact that 0.9(recurring...) is 1It's a limit. Read about them.Skorpy-chan wrote:
No. 0.99 recurring equals 0.99 recurring. It's nearly 1, but not.
Yes, calculus is where this becomes more intuitive, but I didn't learn formal proofs for this until I took a course in Real Analysis.nukchebi0 wrote:
Like I said. Calculus makes understanding this really simple.
The concepts of limits makes understanding how the proofs work easy.SenorToenails wrote:
Yes, calculus is where this becomes more intuitive, but I didn't learn formal proofs for this until I took a course in Real Analysis.nukchebi0 wrote:
Like I said. Calculus makes understanding this really simple.
I've never learned proofs for this either.
Wrong, we will not touch. Even if we did that an infinite amount of times.-=raska=- wrote:
I'm going to link them to an article because I'm too lazy to write the proofs again. The article contains a ton a proofs, all you need to do is read them. Oh and read the section that's about the non-believers, it's pretty good. And as I said in me previous post, if you are going to argue with me that 0.999.. is not equal to 1, at least show me that one of the proofs is wrong.Hakei wrote:
Because that's how it works, instead of refuting what someone says, you're just going to link them to an article.
Wiki this, wiki that.
Fuck deep mathematics, and long drawn out formulas, no matter how many 9's you stick on the end, you're just gonna end up with something close to 1.
Let me ask you this:
If we sit one metre apart, and we cut our distance apart by 9/10ths, and then 9/10ths again and again and again.
Do we ever touch each other?
That's probably why I'll never believe this. Because according to this theory, we would end up touching, no?
Edit: Typo.
And to your question, yes we will touch if we do that an infinite amount of times. This is called the concept of limits. But as you know, its impossible for a human to do something an infinite amount of times. And even if we were able to cut our distance by 9/10th a googolplex times, we wouldn't touch.
In 0.999..., there are an infinite amount of 9's. That's why it equals to 1.
Hakei, take calculus courses, it might help. Unless you come back here and tell us that an integral is an approximation...
edit :noM@rC.ExE wrote:
/win
/fail/winwiki wrote:
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….
and :
http://upload.wikimedia.org/math/6/f/a/ … 162825.png
/win.
In maths it works, in reality it doesn't.
I suppose that's because I am trying to compare a physical process to a theory, which I shouldn't be doing.
In maths .999 = 1 will work, however in reality the 9/10ths thing won't.
Newsflash: Infinity is purely conceptual! You cannot draw parallels in direct human experience.Hakei wrote:
Wrong, we will not touch. Even if we did that an infinite amount of times.
In maths it works, in reality it doesn't.
I suppose that's because I am trying to compare a physical process to a theory, which I shouldn't be doing.
In maths .999 = 1 will work, however in reality the 9/10ths thing won't.
I still don't understand why this is so hard to grasp. Clearly there is some fundamental confusion on what limits and infinity mean. They have been explained, and sources provided so you guys can read further. What is the trouble?
Last edited by SenorToenails (2008-02-10 01:12:37)
Actually, it would work in reality. An atom is only so big. Reach the size of an atom, and there you go you are touching.
Bad reasoning. A limit in this case has nothing to do with ANY physical representation. Logic like that implies that there is some finite number of '9's in the .999... and that there is some .000...1 that follows it. That IS NOT the case.AllmightyOz wrote:
Actually, it would work in reality. An atom is only so big. Reach the size of an atom, and there you go you are touching.
Next stop: neutrinos.AllmightyOz wrote:
Actually, it would work in reality. An atom is only so big. Reach the size of an atom, and there you go you are touching.
And quarks. Or is it the other way round?
Last edited by some_random_panda (2008-02-10 01:21:54)
Talking physically not mathematically. An atom (inside, the quark) is the smallest known piece of matter. In reality, you can't get smaller than an atom. Therefore you would eventually touch. 0.9999 equals one as far as I am concerned. I go by sig figs
those are INSIDE of atoms though.some_random_panda wrote:
Next stop: neutrinos.AllmightyOz wrote:
Actually, it would work in reality. An atom is only so big. Reach the size of an atom, and there you go you are touching.
And quarks. Or is it the other way round?
Last edited by AllmightyOz (2008-02-10 01:24:05)
I'm not splitting hairs, but an atom is not the smallest that matter can get. Try fermions. They are smaller than an atom and have mass.AllmightyOz wrote:
Talking physically not mathematically. An atom (inside, the quark) is the smallest known piece of matter. In reality, you can't get smaller than an atom. Therefore you would eventually touch. 0.9999 equals one as far as I am concerned. I go by sig figs
Last edited by SenorToenails (2008-02-10 01:26:54)
Electrons, neutrons, and protons are all smaller than individual atoms.
Okay, argue as you may, there is still a limit to how small matter than be. And once one goes over that limit, one is touching the other person.
Default to my statement from before:AllmightyOz wrote:
Okay, argue as you may, there is still a limit to how small matter than be. And once one goes over that limit, one is touching the other person.
Stop arguing a bad example.SenorToenails wrote:
Bad reasoning. A limit in this case has nothing to do with ANY physical representation. Logic like that implies that there is some finite number of '9's in the .999... and that there is some .000...1 that follows it. That IS NOT the case.
This is reality not math. There are imaginary numbers in math as well. Square root of a negative number for example. You could never have that in reality.