You dumbass. It's not infinitely close to 2. It IS 2. And it IS a real number, because IT'S FUCKING 2.
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Anonymous2006-08-12 10:50
>>41
gb2/school/
1.999... is a limit, it is not a real number. As you increase the number of 9s, it gets closer and closer to 2. As the number of 9s goes to infinity, it gets infinitely close to 2. 1.999... is NOT a real number, because it is infinitely complex. Nothing in this world has a radius, length, etc. of 1.999...
>>41
You are an idiot. Your argument is that an infinite series (discussed here as 1.999...) is a real number, because it is equal to 2, and 2 is a real number. A SERIES IS NOT A FUCKING REAL NUMBER. IT CAN BE EQUAL TO A REAL NUMBER, BUT IT IS A SERIES, IT'S NOT EVEN A NUMBER.
>>47 >>48
You are both also idiots. As you add more 9s, it becomes closer and closer to 2. With an infinite number of 9s, it is infinitely close to 2. THIS IS THE EXACT SAME FUCKING THING AS SAYING THAT IT IS EQUAL TO 2. IT IS JUST ANOTHER WAY OF SAYING IT BECAUSE IT IS AN INFINITE SERIES.
>>54
The series gets closer and closer to 2, as the number of terms increases. And if you don't think .999... is a series, then you write out all of the 9s by hand, and I'll write out the series notation, and we'll see who finishes first.
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Anonymous2006-08-13 14:26
>>55
Just because we can't write it out doesn't mean it's not a number you fucking idiot. I suppose you don't think pi is a number? WELL FUCKING WRITE IT OUT THEN!
Thanks for completely ignoring the article I posted, jackass. Here, I'll paste the relevant bits for you:
>"0.9999... is a concept, not a number." All numbers are concepts. Some numbers, like 1, have stronger links to reality than others, but we are looking at mathematics here, not the real world. If you're going to throw away numbers which can't concretely exist, then you're throwing away pi, e, i, zero, and, frankly, almost all of mathematics.
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Anonymous2006-08-13 14:59
>>56
I did read it, and I never said that it was concept, I said it was a series. Find a better link, perhaps by someone who actually has credence in the mathematics field, not a 21 year old kid with a BA. Get a brain yourself too, you have no argument other than kopipe.
>>57
Fine, look at Mathworld, probably the best and most accurate math resource on the internet. Here's the article on what a repeating decimal is (with several citations from mathematical books and journals): http://mathworld.wolfram.com/RepeatingDecimal.html
This page clearly states that repeating decimal notation, such as 0.333... represents a NUMBER, not a series. Otherwise how could you write 1/3 = 0.333... if one is a number and the other is a series? The article does not even use the word series; and lastly for great effect, allow me to quote the opening line of the article:
A repeating decimal, also called a recurring decimal, is a number
Case closed.
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Anonymous2006-08-13 20:00
You should have just quoted:
| Numbers such as 0.5 are sometimes regarded as repeating decimals since 0.5 [..] = 0.49...
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Anonymous2006-08-13 20:15
>>61
This is what I like about this article; the article states 0.999... = 1 as a mere afterthought, an obvious, insignificant consequence of the structure of the real number line.
This is about as much attention as that statement deserves in the mathematical community. It's an incredibly trivial result; you won't find a mathematician on the planet who will contest this.
OK a bit of a side track here but honest question here. Why does one of the posters above expressly refer to 1.999.. as a series? I can kind of see the logic to that but it strikes me odd as when I was in school, series always refered to a serires of terms in the summation or product of some sequence or set, not the actual sum or product.
Is it the current education trend to view irrationals as a summation or is it just the guy above?
>>65
Nope, it's just the guy above. He's wrong, very very wrong.
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Anonymous2006-08-15 11:15
Some mathematicians say that .9 repeating equals 1, while others disagree. In truth, it's a number infinitely close to 1 without touching it. However, infinity in itself is nearly impossible to describe or understand. However due to the fact that the numbers are close enough and math still works with the assumption, people will assume .9 repeating to equal 1 unless they want to be pricks.
>>68
Watch yourself, the idiots in this thread don't understand concepts like "infinitely close" or "asymptote".
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Anonymous2006-08-15 12:47
10/3 = 3r1
10/3 * 3 = 9r3 = 10
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Anonymous2006-08-15 20:16
>>68 Some mathematicians say that .9 repeating equals 1, while others disagree.
There isn't a mathematician on the planet that things 0.9 repeating is not 1 in standard analysis. Seriously. I'll give you my first born son if you find me such a mathematician.
In truth, it's a number infinitely close to 1 without touching it.
Again, fail. There's no such thing as infinitely close, and there's no such thing as numbers that "touch", unless they are the same number. This is due to the fact that the real number line is Cauchy complete, sequentially compact, everywhere dense, pick one.
However, infinity in itself is nearly impossible to describe or understand.
Comments like these make me cry. There is so much fail packed into this sentence I don't even know what to say. Here's a methematician refuting this statement, among many others: http://polymathematics.typepad.com/polymath/2006/06/refutations.html
However due to the fact that the numbers are close enough and math still works with the assumption, people will assume .9 repeating to equal 1
*sigh*. It's not an assumption. Mathematics is not this sloppy thing where we sweep our dirt under the table. It is the most rigorous field of science in existance.
Just stay away from these discussions. You have no idea what you're talking about.
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Anonymous2006-08-16 3:48
Yes, mathematics is THE most rigorously defined science in existence. Bertrand Russell's "Principia Mathematica" takes over 360 pages to get to one of the lemmas that will be used to show 1+1=2.
Just because something close to something doesn't mean it IS something.
Rounding is made for simplification, fuckheads. When you're talking about fallacies in logic itself, you need ot be exact. And rounding numbers, even if 9.999 reapeating is pretty damn close to 1, it's not, and it's a simplification.
>>75
fail. read the fucking thread, i'm sick of you trolls
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Anonymous2006-08-20 9:31
1.99999... is a number that can be represented as an infinite sequence: 1+0.9+0.09+... just as 2 is a number that can be represented by the infinite sequence: 2+0.0+0.00+0.000. Really, a sequence is a set of numbers, so how can one number be a sequence? It can be REPRESENTED by a sequence, but it is not a sequence.