0.9999 = 1, true or false and why?
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Yes, but even if it's recurring, it's still not 1. It's an infinite small fraction away from one, but it's not one unless you round.Snork Maiden said:Hence the second line to my postpoiumty said:
as 9y =/= 9.999999Pandairon said:
So you're restating what you've already said there is not need to so other than that it is fine.
Although if you mean 0.9999999recurring = 1 then yes it is.
That still doesn't detract from bad arithmetic. I don't care if he is trying to prove that the moon is made of cheese but 0.9999999 x 10 does NOT equal 9.9999999 not matter if 9 is recurring or not.TZer0 said:
He hem....NimbleJack3 said:Yes, but even if it's recurring, it's still not 1. It's an infinite small fraction away from one, but it's not one unless you round.Snork Maiden said:Hence the second line to my postpoiumty said:
Wow how many times does this go around forums. Anyway I assure you that 0.99' is indeed equalt to one, though many maths graduates still refuse to believe it. It comes down to an understanding of what infinity is. It's pointless to argue against it, as it's been proved mathematically in a rediculous number of ways MANY times, but even I admit it can be hard to rationalise it in your head. If you can't accept the proof given, you've pretty much gotta take my word for it...as the more complex proofs require a high level of mathematical competence to understand....still if you think you are up to it there is a rather good page in the most obvious of places.
http://en.wikipedia.org/wiki/0.999999999
Goddamnit, I'm looking at the simple proofs on Wikipedia and it's disconcerting. I know the maths works out but I keep thinking numbers are dissapearing in there.MPXenon said:He hem....NimbleJack3 said:Yes, but even if it's recurring, it's still not 1. It's an infinite small fraction away from one, but it's not one unless you round.Snork Maiden said:Hence the second line to my postpoiumty said:
Wow how many times does this go around forums. Anyway I assure you that 0.99' is indeed equalt to one, though many maths graduates still refuse to believe it. It comes down to an understanding of what infinity is. It's pointless to argue against it, as it's been proved mathematically in a rediculous number of ways MANY times, but even I admit it can be hard to rationalise it in your head. If you can't accept the proof given, you've pretty much gotta take my word for it...as the more complex proofs require a high level of mathematical competence to understand....still if you think you are up to it there is a rather good page in the most obvious of places.
http://en.wikipedia.org/wiki/0.999999999
Noooooo, not this again!! Last time this discussion went on for 30 fucking pages!!!
0,99999999... is indeed = 1, by the way.
0,99999999... is indeed = 1, by the way.
Really? Because then I had the apparently mistaken idea about a quite well-described paradox called Hilbert's Paradox of the Grand Hotel [http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel]. In this case, we just ask all the guests to go to move to the left (that is, to a room number one higher than their current one).Skarin said:
Anyways, the reason for OP not writing recurring is probably the fact that he didn't quite get what those ... after 0.999 meant.
Because when it is recurring, the proof arguably makes sense.
It is entirely true, assuming you are speaking of an infinite series of 9s following the decimal. There are a number of proofs of varying rigor but the simplest one to understand goes thus:
1 / 3 = .333 (infinite series)
.333 * 3 = .999 (infinite series)
Fundamental rules of arithmatic indicate that, in reversing the process exactly I ought to end up at the same result. Thus, while the result looks different it remains the same.
The trouble people have here is the fact that most people never take enough math to deal with the concept of infinity. A hundred million nines following the decimal doesn't equal one, it just gets incredibly close to one; you literally need an infinite number of nines before the number becomes a tedious stand in for one.
There are other examples of strangely perplexing conceptual problems dealing with infinity, the most famous of which is probably the one regarding an object approaching a finish line while that slows as it approaches. In the simplest form, in one measure of time, the object closes half the distance to the finish while in the next equal measure of time it covers half the remaining distance again and the question becomes will the object ever reach the finish line. The question is perplexing because it has two entirely correct answers. Given infinite measures of time the object will, in fact, reach the finish line as it is simply an infinite geometric series and as such has a predictable outcome at infinity in this case (the result converges to put it explicitly). But this entirely correct and technical answer isn't actually all that useful because no matter how short our arbitrary measure of time, it is safe to say that you don't have infinite units of it to see if our object reaches the goal. As such, one can say the object will not reach the finish line in any reality we care to measure.
The same is true of this problem. While the concept is simple and the proofs myriad, people have trouble accepting the proposition simply because we cannot concepualize infinity. One can examine the proofs and find that while some might lack rigour, the totality of evidence clearly points to the fact that .999 is indeed 1, or they can simply accept is as something that's true and have a dorky bit of trivia. There is a standard caution - unless it is explicitly stated that you have an infinite series of nines, one cannot assume the result equals one. In standard notation, when a series is known to repeat, one must first write out one entire portion of the pattern and append a horizontal bar across the last digit. When one does not have access to such things, they need to work out another ways of clarifying themselves.
1 / 3 = .333 (infinite series)
.333 * 3 = .999 (infinite series)
Fundamental rules of arithmatic indicate that, in reversing the process exactly I ought to end up at the same result. Thus, while the result looks different it remains the same.
The trouble people have here is the fact that most people never take enough math to deal with the concept of infinity. A hundred million nines following the decimal doesn't equal one, it just gets incredibly close to one; you literally need an infinite number of nines before the number becomes a tedious stand in for one.
There are other examples of strangely perplexing conceptual problems dealing with infinity, the most famous of which is probably the one regarding an object approaching a finish line while that slows as it approaches. In the simplest form, in one measure of time, the object closes half the distance to the finish while in the next equal measure of time it covers half the remaining distance again and the question becomes will the object ever reach the finish line. The question is perplexing because it has two entirely correct answers. Given infinite measures of time the object will, in fact, reach the finish line as it is simply an infinite geometric series and as such has a predictable outcome at infinity in this case (the result converges to put it explicitly). But this entirely correct and technical answer isn't actually all that useful because no matter how short our arbitrary measure of time, it is safe to say that you don't have infinite units of it to see if our object reaches the goal. As such, one can say the object will not reach the finish line in any reality we care to measure.
The same is true of this problem. While the concept is simple and the proofs myriad, people have trouble accepting the proposition simply because we cannot concepualize infinity. One can examine the proofs and find that while some might lack rigour, the totality of evidence clearly points to the fact that .999 is indeed 1, or they can simply accept is as something that's true and have a dorky bit of trivia. There is a standard caution - unless it is explicitly stated that you have an infinite series of nines, one cannot assume the result equals one. In standard notation, when a series is known to repeat, one must first write out one entire portion of the pattern and append a horizontal bar across the last digit. When one does not have access to such things, they need to work out another ways of clarifying themselves.
The last thread about this [http://www.escapistmagazine.com/forums/read/18.85789?page=1] ended up going to 30 pages. The definitive answer is that it's not any kind of trick (like those "0=1" proofs are), just a quirk of how we represent numbers. I'm going to sink this thread so y'all can talk about it if you'd like but discussion can kinda peter out naturally...
-- Alex
-- Alex
Isn't it the other way around?! Logically we can see that there's negligible difference but mathematically they aren't the same.reg42 said:
No I've just understood the question, forgive me you are correct!!
You went wrong in the first step. 1/3 is an irational number, you can't express it as a decimal.Leon said: