What if we have only number 9?
Thursday, September 13th, 2007.
Truely geeky clock design. Thanks to Ernie for the submit.
@ haha.nu.
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(53 votes, average: 4.55 out of 5). 
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September 14th, 2007 09:24
Most are legit, but 7 is kinda cheating, imo
September 14th, 2007 10:32
Actually, .9 repeating is mathematically equal to 1.
September 14th, 2007 11:30
.9 repeating is not equal to 1 that is a common misconception, you have to get a deeper understanding of infinity!
September 14th, 2007 11:57
Chris, .9 repeating represents the same number as the symbol 1. Feel free to check it up from Wikipedia or any elementary analysis course book. Your deeper understanding of infinity is erroneous.
September 14th, 2007 13:15
A better answer for 7 would have been sqrt(9)!+9/9
September 15th, 2007 13:08
.9 repeating is NOT 1. For example a recognized mathematical problem is:
“1>X, what is greatest possible value of X?”
If what you said is true, the largest possible value of something less than 1, is 1. Does that compute anywhere?
The problem is, like the first guy said, you do not understand your infinity.
September 15th, 2007 14:58
Well actually jambo is correct as if you take the limit of .9 repeating you obtain 1. Thus it is said to equal 1.
September 15th, 2007 14:59
Well actually jambo is correct as if you take the limit of .9 repeating you obtain 1. Thus it is said to equal 1.
September 15th, 2007 15:09
Masterfrog, what you’re explaining is the notion of boundaries. What you’re trying to say (I think) is that if X
September 15th, 2007 17:16
The set of values satisfying “1>X” does not have a maximal element. So the answer to your question is there isn’t a greatest possible value of X.
If this seems like cheating to you, ask the opposite question – “For X>1, what is the maximal value of X?”. The answer to this question is “None” as well.
September 15th, 2007 19:46
I could be mistaken but couldn’t you just put a “9″ at 9 o’clock? There is no need for the equation.
September 15th, 2007 20:23
1/9 = 0.1111111111′
0.111111111′ x 9 = 0.9999999999999′
Therefore 0.9999999′ = 1 / 9 * 9 = 1
September 15th, 2007 22:17
another way to express it is…
x = 0.9 repeating
10x = 9.9 repeating
10x – x = 9.9 repeating – .9 repeating
9x = 9
x = 1
September 15th, 2007 22:18
NERDS!!!!
September 16th, 2007 00:47
yes NERDS!
September 16th, 2007 00:50
You all need hobbies and girlfriends…
September 16th, 2007 08:47
its an old one i first saw this years ago,and its shopped
September 17th, 2007 02:54
1/3 = .333333333(repeating)
2/3 = .666666666(repeating)
3/3 = .999999999(repeating)
3/3 = 1
solved.
September 17th, 2007 14:33
omfg
you all crack me up
September 17th, 2007 15:50
1 = 0.99…
Exact proofs have been posted above, but this can easily be seen by Archimedes’ Axiom: when working in the set of real numbers, if one constructs an array of intervals which all contain each other and get smaller, at least on element exists that is in all intervals.
Hoe one can see this applicated to this problem, if one constructs the interval from 0.99… to 1, and one tries to constructs a smaller interval, one notices that this is not possible. Which number larger than 0.99.. is smaller than 1? One could say: add a 9 at the end, but one can’t forget we already have an infinite number of nines. One could conclude that such interval can’t be made any smaller and thus 0.99… = 1, because there is no number between the two. Between every other number, there is always another number: 1.5 and 1.6; in between we have 1.55 for example. Between 0.99.. and 1 we have no number, thus both represent the same number.
Also infinity has nothing to do with this problem, except that we have an infinite number of digits (but this only is a consequence from our numerical system, other systems have the same repeating constructs with 1/2 (a ternary numerical system, for example)).
The example Masterfrog gives, is the notion of a supremum. There is no number that satisfies the equation x = max{i | i = 1}. Please also note that this is some form of contraposed form of your equation: since we can’t find the maximum value which satisfies your equation, we look for the smallest which doesn’t satisfy your equation. (A therefore B, thus not B therefore not A). While this is mathematically not perfectly correctly expressed and contains a small nuance, this is the limit of your question
September 18th, 2007 06:08
.9 repeating is equal to 1 no matter how much you want to deny it. There’s plenty of proofs out there (most simple) that show it. Or, you can just look at 9/9.
Anyway… I like the one poster’s suggestion: sqrt(9)!+9/9… that’s pretty nice!
September 18th, 2007 22:32
I wish I knew more than basic algebra. Does anyone know where I can download video courses for more advanced mathematics than that? Free preferably.
September 19th, 2007 21:28
I hate to say it. But 0.99 repeating is not equal to one. The LIMIT of 0.99 repeating is equal to 1. It approaches 1, but never gets there.
saying 0.999 and 1 are the same is kind of like saying 1 is the same as 2 because you believe the space between them is insignificant. No matter how small the space is, even if that space is infinitely small, it is still a separate number.
It is for all intensive purposes equivalent, but not equal.
This distinction and error of common mathematics is why we cannot solve problems like the Riemann hypothesis. Our understanding of math is wrong, weve made an assumption that was incorrect and have all accepted it as truth,
Masterfrog shows us why this assumption is wrong. 1 > X The largest X can be is not 1.
If you code in C you will realize making this assumption will cause programs to fail. It cannot be assumed as truth. Even if the equations prove it… the equations cannot handle infinities. In fact there is a separate mathematics dealing with infinities and it does not follow standard algebra.
when dealing with numbers we cannot precieve, whole numbers fail.
September 20th, 2007 01:00
No matter how you look at it, the equation listed for 7 o’clock is accurate to the margin of error inherent in the width of the clock hands, so the argument is effectively irrelevant to this application! That having been said, I enjoy the discourse, carry on.
September 20th, 2007 10:30
x –
.999 repeating IS a limit. It is redundant to say “the limit of .999 repeating”.
Specifically, .999 repeating is the limit as n approaches infinity of [Sum from i=1 to i=n of 9/(10^i)]. In addition, a limit is not a process – it isn’t trying to “get” anywhere. There isn’t a little man who keeps attaching 9s to the end of .999, trying desperately to get to 1. A limit is a concept. It represents an idea, not a process. The specific idea .999 repeating represents is the symbol 1
As someone else already pointed out, there is actually no value of X that you can pick to be the maximal element less than 1. Think about it. The moment you specify any number, you can immediately average that number and 1 and get a new number even closer.
Mathematically, there is absolutely no way to distinguish between .999 repeating and the symbol 1. It is merely a matter of notation. I don’t know specifically what instances of coding in C cause programs to fail if you treat .999 repeating as 1, but realize a computer cannot actually deal with .999 repeating infinitely. It has to stop at some point and round or truncate.
September 20th, 2007 12:17
Let me sum this all up for you.
NO-BODY-CARES.
September 20th, 2007 17:40
> Let me sum this all up for you.
> NO-BODY-CARES.
Ahh yes. . . a common idiot adds their two cents worth to an intellectual discussion. I’m surprised it took that long. Maybe there’s some Brittney Spears news you can read instead.
September 21st, 2007 06:16
well..eehhh…i guess my opinion won’t really help you resolve the dispute between 0.9999…. and 1, but i do have a suggestion…
……BUY A NORMAL CLOCK!
September 21st, 2007 08:38
hey, sorry to interrupt the flow, but happy peace day guys. spread the word
September 21st, 2007 12:55
When you are coding C if you assume that .9 repeating is 1 you would expect for example one more cycle in a “while” expression.
so 1 is 1 and .9 repeating is something else
September 24th, 2007 06:31
I stopped reading X’s post as soon as I got to “all intensive purposes”.
Isn’t the saying “all intents and purposes”?
I would agree Daniel and Egon. The proofs above by Dude and Alec are both valid.
mister x, what a computer tells you is not always true. As Daniel implied, a “while” expression in C is limited by the precision of the numbers that a computer can evaluate. Any attempt to store a number with an infinite number of decimal places (like 0.999…) in a computer will necessarily cause the number to be truncated, or the computer will run out of memory trying to handle it.
As such, your C program will not be telling you that 0.9999…
September 24th, 2007 19:06
At 9 o’clock…they couldn’t just put a 9 by itself!?
September 25th, 2007 09:16
isn’t this .9′ thing like the theory that you can’t reach a destination in that you get half way and then half of that an infinate amount of times.
September 26th, 2007 02:23
If you’re really interested in these kinds of questions, try “Infinity and the Mind’s Eye” by Rudy Rucker. It is a very interesting book that speaks about all sorts of infinities, both large and small (no, that’s not a hypocrisy). It is well written and not too math intensive either, check it out.
September 26th, 2007 02:25
Sorry, I meant “Infinity and the Mind”
September 26th, 2007 08:28
are you kidding me? why are people actually arguing about this? i guess the internet brings out all types…
get a life. its called outside. see it? its right there. don’t be afraid. the sun won’t burn your pale skin.
September 26th, 2007 14:30
My favorite proof:
x=.999~
10x= 9.999~
10x-x=9.999~-.999~=9
9x=9
x=1
.999~=1
If you still aren’t convinced, wikipedia has a bajillion proofs: http://en.wikipedia.org/wiki/.999#Proofs
September 26th, 2007 15:32
…and to drag up stuff from the (recent) past:
someone mentioned that 1/3=0.333333333…
Um. It doesn’t. It’s an approximation. Just as 1 approximates 0.99999…
It’s just a rough (well, I suppose it’s not THAT rough) estimate so you can use non-fraction equivalents (word used loosely).
And to point out something else: It seems that there are three instances of 9 in every representation here, so plunking a 9 down by itself for 9 o’clock is kinda cheap. Although they could have gone the 9×9/9 route.
September 29th, 2007 18:48
There are 1.9… repeating kind of people :
Those who understand elementary mathematics and those who don´t. ;()
No one seems to be aware of the importance of the three dots … this means infinitely repeating, that´s why .9…repeating is EXACTLY equal to 1.
As we say in my country: dude grab some books, they won´t bite you.
Have a nice day. Greetings from Buenos Aires, Argentina.
October 3rd, 2007 17:03
WOW OMG OMG WOW OMG. 1 IS NOT EQUAL TO .999…
October 3rd, 2007 20:16
Lols, I love the kids spamming omgs get a life, go outside etc etc.
Do you realize you wouldn’t even be using a computer right now if it weren’t for ………
Nevermind.
October 4th, 2007 00:01
You guys do know that math is completely false, right? I mean it’s so close that it may as well not matter, but any system where .9999 = 1, or is counted as the same thing, is wrong, no matter how you slice it. ‘S why I failed math.
October 4th, 2007 07:11
Math isn’t completely false, theres just some things that don’t seem to make sense to us. .99 repeating approaches 1, it never reaches 1. Only after rounding up can it be considered EXACTLY 1.0
It’s best just to ignore the spammers saying get a life or whatever. They won’t get anywhere in life so just leave them alone. They’re too young or ignorant to realize that theres more to life then having a girlfriend or playing outside..If we all were like them we still would be living in caves.
October 4th, 2007 07:35
1 does not equal .999…
In fact, x.999… and x + 1 are the only 2 numbers that can actually be defined as completely different, since these are the only 2 exact values.
Don’t believe me? Name a value between 0.999… and 1. You can’t, because, no matter how far you go towards infinity, there will always be 1 (unit) between 0.999… and 1.
Thus, since .999… and 1 are the only 2 infinitely defined values, and they are not equal, then, no matter what, they will never be equal.
Cheers,
-Finn
October 4th, 2007 08:03
Okay, so in the “spam protection” section of this form, it asks me for the the sum of 1+4. When I originally put 4.9…repeating, it did not accept my comment. So the internet doesn’t agree with you. Also, sqrt(9)!+9/9 is exactly what is used for 5, except plus, so that’s boring and we never would have had this discussion. Also, the sun will burn my pale skin.
October 5th, 2007 06:52
Chris, you can’t type .9 repeating into any text box, no matter how big. You have a very basic understanding of math, if any. .9 repeating is equal to one, look at the wikipedia article, they talk a lot of sense.
Finnboghi, you can’t name a number between .9 repeating and 1 because they’re the same number, not because there’s always a number in between them. It’s basic calculus.
October 6th, 2007 01:32
You people fail at life.
0.999 repeating = EXACTLY 1.
dont try to act smart. your not.
most likely your a fat american ass hole who is too ignorant to know where america is on the globe
@ the guys who say “Go outside” etc etc: you are clearly NOT outside yourself. take your own advise, it will make the internet a better place.
kkthxbai
October 7th, 2007 06:39
Nick… you make me laugh. You’re pretty much an idiot yourself. At least most of the people posting comments know how to spell. Take a look in the mirror before you go calling people stupid, especially with that retarded “kkthxbai” bull shit. You probably think that makes you cool so it automatically excludes you from being an idiot like you claim the rest of us to be.
October 7th, 2007 16:33
Well thomas, clearly you are so ignorant that you dont know that that phrase is used as dismissive sarcasm when the argument is obviously one with people such as yourself.
And yes. yes it DOES make me think i’m cool – thanks for pointing that out (H)
October 8th, 2007 08:27
That one works because the smallest amount of interval that time may exist at is 1.855×10^-43 second intervals. Thus, despite there being an infinitely small difference between 0.9… and 1, it is physically insignificant (and nonexistent when) when dealing with time.
October 8th, 2007 18:49
Ok two things
1.) I respect you all because not only are you fucking amazing mathematicians, but you can argue in a semi respectful way.
2.) Are there any girls who have posted here other than me?
October 8th, 2007 22:08
Aaron:
“‘S why I failed math” does not exactly inspire confidence in your arguments.
October 8th, 2007 22:50
okay let me just state one thing for all the “normal people”
getting pussy
does not
stop people
from being smart.
fuck
off
October 9th, 2007 01:18
.999 repeating equals 1. yes really, i have a masters in electrical engineering.
i also have a girlfriend and got laid after partying down this weekend.
throw that wrench in your “normal person” spokes and die.
oh, and nick, im american. fuck you and your prejudice rhetoric.
Nice post! i want one.
October 9th, 2007 01:45
you can’t really express .9 repeating mathematically without using limits in a decimal fashion that I can think of so, to produce .9 repeating with an arbitrarily large number of digits you would take the summation of i = 0 to n (where n is the number of digits you want to tack on) of 1/(9 * 10^i)
since that doesn’t repeat 9 infinitely you would have to take the limit as n -> infinity:
limit as n approaches infinity of the summation of i=0 to n of 1/(9*10^i)=.9 repeating (visually)
when you actually evaluate that limit (which I shall call the limit), you get one, so by substitution 1= the limit, the limit = .9 repeating, therefore 1=.9 repeating
hmm I seem to have rambled a bit there, but I think that might stop any more arguing. by the way, I’m surprised that no one mentioned plank’s constant before jason.
October 9th, 2007 02:54
Okay, I’ll bite.
How much less is .999… than 1?
I’m reading a lot of “approaching”s and “getting close to” verbage here, but that makes no sense. Numbers don’t move, they don’t approach, they don’t grow, they don’t wistfully pine for the fjords which they left behind to pursue a life in the big city, only to find their dreams crumpled in the gutter like so much New Year’s confetti.
So, until someone can tell me the exact difference between .999… and 1, I’m going to have to go with Archimedes and um, every other mathematician in the world.
October 9th, 2007 05:03
“someone mentioned that 1/3=0.333333333…
Um. It doesn’t. It’s an approximation.”
Really? I’d like to see an explanation of that.
October 9th, 2007 05:23
Jonathan H. said
[i]someone mentioned that 1/3=0.333333333…
Um. It doesn’t. It’s an approximation.[/i]
Really? I thought that when you divide 1 by 3 you get a decimal and threes repeating. No approximating necessary if it is specified that the threes repeat. Unless there is some deep mathematical truth that my fourth grade teacher neglected to share.
October 9th, 2007 05:51
This comment number is 9 * 9 – 9 * √9
October 9th, 2007 05:59
Keep up the good work!
October 9th, 2007 06:46
0.9 repeating = 1 is taking the easy way out.
October 9th, 2007 07:40
One final proof using the ideas of limits, derivatives, and l’Hôpital’s rule:
Let’s say you have the function f(x) = [1 - 1/(10^x)]. If you’ll note, the larger x gets, the smaller the number 1/(10^x) gets. A few of the numbers are:
1/(10^1) = 1/10 = .1
1/(10^2) = 1/100 = .01
1/(10^3) = 1/1000 = .001
And so on. Now when you have 1 – 1/(10^x), the numbers follow a similar pattern:
1 – 1/(10^1) = 1 – 1/10 = .9
1 – 1/(10^2) = 1 – 1/100 = .99
1 – 1/(10^3) = 1 – 1/1000 = .999
And so on. Now if you’ll allow x to get infinitely big, the number of 9s following the decimal becomes infinitely big (.999…). We can demonstrate this in the form of a limit:
lim [1 - 1/(10^x)]
x->oo
Now turn 1 into (10^x)/(10^x) and with a little simple math you’ll get
lim [(10^x)-1] / (10^x)
x->oo
If you were to take the limit of both the numerator and the denominator as x->oo you’d essentially have oo/oo.
l’Hôpital’s rule states that if the limit of the function results in 0/0 or oo/oo you can take the derivative of the function. If we take the derivative of our function, we would get:
lim [(10^x)*ln10/[(10^x)*ln10
x->oo
The rate of increase of the numerator and the denominator is equal, and therefore equals 1. And the limit of a constant is that constant.
Hence .999… = 1.
October 9th, 2007 08:22
Amen punisher.
Whoever thinks nerds and geeks don’t get laid should stop watching dated sitcoms and actually get out into the real world
I’m no mathematician, but .9 repeating and 1 are not the same thing. The problem isn’t with math, the problem is with us. As finite beings, humans aren’t equipped to deal with dilemmas concerning infinite properties.
score one for evolutionary philosophy ;D
October 9th, 2007 08:26
Hey, i just read all the posts and i find it really funny that a clock add thing turned into a huge mathematical discution.
Now i just want to add my 2 cents.
Someone earlier said that .99999~ is a limit. that is compleatly correct, the limit of X when X tends to .99999~ would be 1 however as that person said it would never reach it, in fact if you where to make a graph of this you would very graphicaly see that there would be a cut in the line since the place where the value of one would be would not be drawn in the graph.
Now, mathematics is divided in 2 Big Branches (not saying there isn’t any others) Arithmetics and Calculus, now, for the arithmetical point of view .9999~ could be taken as 1 why because the interval between the two numbers is so small that its practicaly 0. this is also a limit that would be that when X tends to .99999~ to infinity the diference of 1 and that would be 0 ok, now in calculus that would not apply in that exact way because the basis of calculus is that you are making a series of additions between limits and makeing them smaller every time to be able to ger a more acurate result, how ever if a limit does not exist then you would have an error or would have to break the ecuation into 2 this means that for it to be able to work the limit of any eccuation must be true for every value of x. In conclution what im saying is that the limit of .999999~ while it does tend to 1 and will invariably come as close as infinity to that number, it will never be quite 1.
Sorry for any bad vocab, not an english speaker.
I hope this can helps
October 9th, 2007 09:41
Yes and no…(repeating)
October 9th, 2007 12:37
1 is a strange number.
October 9th, 2007 13:32
to solve all the crap about number 7.
why not use 9-(9+9)/9
October 9th, 2007 13:34
I have a total and complete understanding of an infinite number of infinities, and I must say that you are all correct, just in ways your human minds cannot possibly begin to comprehend.
October 9th, 2007 14:09
Clearly most people don’t understand the concepts of math. I even remember the class in grade 10 where the teacher stopped doing the lesson he was teaching , just to prove to us that .999 =1
If anyone took 5 minutes to research this information on say Wiki, You would find it to be true and this debate would end.
As for the little kiddies and flamers and spammers , etc.
Go to hell.
I’m impressed to see so many people have a discussion about something that requires more then 2 brain cells to process, and not start talking to each other in leet or something stupid such as that.
As for the original reason this reply is to be made.
A very intereting concept for a clock, however it is a little nerdy.
October 10th, 2007 03:14
You all are retarded.
1 > .99 repeating.
.9∞9 is .0∞01 less than 1.
3/3 ≠ .99
2/3 = .66 Yes
but 3/3 = 1
NOT .99
there are not proofs, they are mathematical paradoxes.
October 10th, 2007 08:35
I take this for a spin, even though I’m not a hardcore mathematician like some of you!
Someone before made the point that there’s no little man furiously tacking 9s at the end of .9 repeating. But what if there were? And what if, upon asking “What is the iterval between .9 repeating and 1?” a second little man were to pop into existance to assemble that number?
Of course, for the first few 9s it would appear obvious:
.9
.1
.99
.01
.999
.001
But after a while, and the little dudes get up to speed, it would quickly become clear that the difference between .9 repeating and 1, was .0 repeating, since the second little guy could never hope to get far enough ahead to plant his ‘1′ and the end. Of course 1 – 0.0 = 1.
I have a hard time accepting that this is true, and it is still possible that our limited human intellect simply cannot grasp such things as infinitly small differences, but there are for more proofs arguing that .9repeating = 1 than against it. In fact, most of the arguments against it consist of “Nuh uh, it is so different!”
October 10th, 2007 15:09
“Duff
October 10th, 2007 03:14
You all are retarded.
1 > .99 repeating.”
Okay. Let’s say for a minute that those of us on the other side of the fence concede to your argument. The only question that remains is “How much less is .999… than 1?”
If 1 and .999… are both real and rational numbers, then they therefore could both be put on a number line. Since .999… is less than 1, it would obviously appear to the left of 1 on a number line.
My question is this: “What do you have to add to .999… to get to 1 on that line?” Obviously .1 won’t work. Nor will .01. .001 would still give you a sum greater than one. .000… repeating is nothing, so that can’t work either. I conclude that the only possible number would be an infinite string of zeros, with a one tacked onto the end. This is of course impossible however, since an infinite string by definition has no end.
There is no number that can be added to .9 repeating to make it equal to one. .999… is a number that represent a static, permanent value. It does not approach 1. It is not getting closer to 1 as we speak. It is fixed, static, locked into position on the number line. IT is not creeping closer to 1. It is 1.
Just as surely as the Earth spins round the sun, .999… is exactly equal to one.
October 10th, 2007 16:46
I can prove 1=2.
See how I did it and realize my intent.
http://c2global.com/bin/math.html
http://c2global.com/bin/math.html
October 10th, 2007 18:42
Geeks.
October 10th, 2007 20:09
That proof is invalid, and unrelated to the argument at hand.
The step which says: “Dividing by x – x gives x = x + x” is invalid.
X – X = 0. You cannot divide by (x – x) because you cannot divide by zero. The proof fails.
October 11th, 2007 02:33
Is it just me, or is the equation for 3 o’clock somewhat superfluous? Can’t they just go sqrt(9) instead of adding 9, and then subtracting 9 right away? Instead of sqrt(9)+9-9, can’t it just be sqrt(9)?
October 11th, 2007 03:30
Math is a human construct that is inherently flawed, because like all human constructs (language, art, etc.), math is a metaphor for reality. For example, when we say that an object is “red” in color, our inclination is to comprehend the object as possessing some quality or characteristic that makes it “red” – the “reality” (if you can call it that, and by “reality” I am speaking of the common usage of the term) is that light hits the object, which is reflected into the subject’s iris, which is then transformed through biological and neurological process and filtered through the range of individual human experiences by the subject’s experiences in such a manner that the understanding of a “red” object is then PROJECTED onto the object. Because this is an event that is easily replicated, and because there tends to be agreement on the outcome by most people which is communicated to each other as a consensus, it becomes a reality. This is a very simplistic explanation (sorry) to a very complex philosophical matter, that being the very nature of reality.
Alas, I am off the subject at hand…in the same manner, mathematics is an agreed upon language of sorts that describes reality, but not with the kind of precision necessary to actually DEFINE reality. This is evident in the very simple calculation of 1/3 = .333…. and other mathematical formulae that result in infinite strings of numbers (such as pi). It would take a calculator as big as the universe itself to provide definitive answers to most problems that math seeks to answers – lacking that, numbers are rounded off and we end up with stuff like Lorenz’ butterfly (and so on)…
So, that being said (and much more unsaid), I think that the reason that people have problems with 1=.999… is that they are projecting some type of absolute reality (they see “1″ as somehow being tangible) onto the number “1″ and rejecting the notion that anything other than “1″ can be “1″; “1″ is not “.999…” in the sense that “1″ is not “1/1″, but we all know that they “mean” the same thing. What is lacking is a consensus in “meaning” that prevents some people from accepting “1 = .999…” as being a reality. This may be difficult, if not impossible, simply because most people don’t understand the concept of math as a metaphor and therefore cannot come to grips with the seemingly paradoxical ideas that are “real” in math.
Basically, “.999…” is a concept, and not a “real” number (”real” as in “REAL”, not the mathematical definition; perhaps the phrase “tangible” should be substituted for the word “real” here, but then how to account for the term “number”?); however, “1″ is no more real than “.999…” (or any other number for that matter): they are both concepts. The (quite frankly AMAZING) proofs offered by the astute mathematicians here simply “prove” that one concept is equal to the other, the same as if to prove that 1 = 1/1.
Really, it’s quite simple when you think about it this way. For me at least.
October 11th, 2007 18:40
ok… so if i got the whole thing right as we add more and more 9’s after the decimal, the number gets bigger and bigger(with smaller and smaller increments). And taking into consideration that the number of 9’s after the decimal is infinite, you can say that 0.9… = {1, 2, 3… infinity}
prove that, why don’t you! (i’m kidding I know this is stupid) but that would mean that irrational numbers like pi and e and sqrt(2) and others would be equal to the first natural number that follows (or what do they call it in english.. you know like 1, 2…) ex: pi=3.14…=4 because it has an infinite number of… numbers after the decimal…
October 21st, 2007 03:00
.9 repeating does equal one and it’s not that hard to confirm ffs.
1/9 = .1 repeating
2/9 = .2 repeating
3/9 = .3 repeating
etc…
9/9 = 1, and logic says that it also equals .9 repeating as any other digit divided by nine equals that digit repeating after a decimal.
October 22nd, 2007 19:33
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nice clock
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October 22nd, 2007 19:34
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nice clock
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October 24th, 2007 07:12
I totally agree… not precisely the Golden ratio,but nice clock
October 24th, 2007 15:46
I think most of you are missing the point.
The much disputed 7 might in fact not be placed at the exact position where it is supposed to be on the clock itself.
Besides, this clock only measure in seconds anyway so why bother if the time is 7:15 or 7:14,999999999?
October 26th, 2007 06:17
Its interesting that the people who think (know) that 1 is equal to 0.999… have produced several proofs to support their argument.
The people who think that 1 is not equal to 0.999… have failed to include any proof whatsoever.
I know who I would believe if I didn’t know already.
October 28th, 2007 01:49
LOL at the guy who spelled asshole as two words.
.999′ is not 1. It is very close to 1 but is not 1.
October 28th, 2007 01:52
Mark, if you need a proof to figure out that .9999… and 1 are not the same then you might also need a proof that 2 + 3 doesn’t equal 6.
October 29th, 2007 21:13
MATH FIGHT!!!!!!!
October 30th, 2007 01:48
“Adisharr
October 28th, 2007 01:49
85
LOL at the guy who spelled asshole as two words.
.999′ is not 1. It is very close to 1 but is not 1. ”
How much less is it then, exactly?
November 1st, 2007 00:18
i find it interesting that all the numbers have three nines except for ‘1′ and that is conveniently blocked by glare…hmmm…
November 13th, 2007 06:37
Nice clock, cool concept, but for 9o’clock why can’t they just use 9? correct me if im wrong but the idea was to make a clock using only 9s.
December 26th, 2007 23:30
This is an interesting thing because of the fact that people of different ages and experiences have different opinions about it. And yes, for the sake of having some mercy I did say opinion.
Small children can’t understand how something as simple as 1 and complicated as .9 repeating can be the same.
Then there are those that have used a calculator and gotten results like 1/3 = .3 repeating and try to “explain” this matter as if the numbers were truly the same rather than a numerical approximation. The 1-line calculator displays the result like that because it has no better means to do it.
Then there are the “proofs” that merely rely on the fact that they have already assumed that approximated numbers equal to the precise ones. They are written by people that have seen the proofs and can’t themselves see how they fail.
Then there are people that have further studied this problem and clearly have mixed opinions about it.
If you imagine “zooming in” the very “last” (allthough there’s not really a last one) 9 of the .999…999 sequence. Clearly this is not the same as 1.000…0000, something is missing. if you would just add .000…00010 to it, it would make sense. But no, some IDIOT adds .000…00009 pushing the problem further.
People that ask what is 1 – .9 repeating, it’s not 0, it’s .0000…0001. While to any practical application that is zero as well as .9 repeating is 1, to a mathematician they are not equal. You can say .9 repeating “is approaching” or “is approximately” 1 and they are proper mathematical consepts, but you go and draw = sign between the 2 on your exam and you’ll get slapped.
January 26th, 2008 08:27
I Stumbled here. The comments are priceless. I will be directing the Math teacher on my campus to your site. As an English teacher, I have an imperfect understanding of what is going on.
February 28th, 2008 03:54
to Chris, who said that the spam protection did not accept 5.99999… as equal to 4+2, i said 13.0 for the sum of 6+7, but the computer did not take that, even though it is equivalent. therefore, Chris’ argument must be disregarded
March 6th, 2008 08:49
wow. i thought i was a geek. but yea, .9 repeating is one in my book.
March 29th, 2008 13:40
Here is a Google Gadget that uses the same clock
http://scripts.tropicalpcsolutions.com/html/gadgets/9clock.html
April 26th, 2009 23:54
I believe these comments can be summed up by one comic.
http://xkcd.com/386/