What about 0,4999...=0,5 or 0,00...(infinite zeroes)...1 = 0?
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Anonymous2006-08-05 16:07
yes
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Anonymous2006-08-05 16:08
no, no nononononon.
0.49999... is not and will never realy be equal to 0,5. There are just cases where you have to declare 0,49999 to be equal to 0,5, but that causes unprecise calculations.
>>3
1+2 is not and will never realy be equal to 4-1. There are just cases where you have to declare 1+2 to be equal to 4-1, but that causes unprecise calculations.
Take for example, 0.5 and 0.55: they are not "the same". But they are not "different" because you don't write them the same. They are "different" because from a mathematical point of view, you can choose an arbitrary value, say epsilon and prove that |0.55 - 0.5| > epsilon. This is true for all numbers that are "different", just a matter of choosing a epsilon "close enough" to 0.
However, for 0.4999.... and 0.5, there is no such value for epsilon. No matter how close to 0 you choose, |0.5 - 0.4999...| will be less than that value. There's a bit more to it but this is the jist of it. Mathematically 0.4999... and 0.5 are the "same".
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Anonymous2006-08-05 22:55
With that said, while 0.4999.... = 0.5, 0.00..1 != 0. The fact that you can appoint a 1 at the end of the decimal expansion means that there is no "infinite zeros" so it's not the same case as 0.4999... and 0.5
>>6
0.00..1, or whatever you want to call it, is not zero so long as the ellipsis represents finitely many zeros. The fact that you can write a "1" to the right of a "..." does not mean, though, that you can stick things on the far end of an infinite series. Just because you can write nonsense doesn't make it true. I conclude that your point is wrong or irrelevant here.
>>9
Why are two numbers different? Because there is a difference in value. So let's say you have a "difference threshold", a really, really small number. If the difference between two numbers is greater than this threshold, then the two numbers are different and they are the same otherwise.
OK so say that threshold is 1/1000. The difference between 2 and 1.9 is greater than this value right? So they are different. Same for 2 and 1.99 right? But 2 and 1.9999 is less than our threshold, so let's just choose a smaller threshold, 1/10000000000 and now 2 and 1.9999 satisfies our requirement to be different. For any two numbers that are difference, there's some really small value that's less than their difference.
But between 2 and 1.999..., there is no such small number.
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Anonymous2006-08-06 22:36
is this the matrix?! is anything REAL? or is it all just non-real? math is false, they just make you BELEIVE in thier system...
GTFO math shitcocks
.9999999... |= 1
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Anonymous2006-08-06 23:26
>>17
For two things to be different, there has to be a finite difference between them, right?
There is no finite difference between .9999..... and 1. Now kindly stop trolling, we've had this debate before
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Anonymous2006-08-07 4:53
The argument that 0.499... is the same as 0.5 is the exact same argument for 0.0....1=0. Since: 0.5-0.4999=0.0...1 if you say that 0.5 and 0.4999... are the same then 0.0...1 and 0 are the same. (same for 2 and 1.999...).
You just need to understand that 0.0...1 is so small that in reality it is 0.
No matter how many zeroes you add it is still a number with finite length. You're arguing it should be rounded off to 0.
0.49999...
This is 0.4 + SUM[N=2 to infinity]( 0.9/(10*N) ). Do the math, it's 0.5. If you haven't learnt limits or infinite series yet, stay in school.
The original premise is "0,00...(infinite zeroes)...1 = 0"
another way of writing that 0.00...(infinite zeroes)...1 is:
5-(0.4 + SUM[N=1 to infinity]( 0.9/(10*N) ). It exactly the same according to sequences and series. SO if you say that 4.999 is 5 then 0.000...1 is zero.
wanker. I'm still not sure why you can't see that the two arguments are identical.
Furthermore, in practical math such small no's as 0.000...1 are irrelevant and considered 0.
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Anonymous2006-08-07 8:25
>>23
Buddy, there is no other way to write it. It's not a valid number in the first place. 5-(0.4 + SUM[N=1 to infinity]( 0.9/(10*N) ) evaluates to a transcendental number, of the irrational set. If it could be evaluated to something that can be written as a terminating decimal, you're implying that it's a rational number. That's your contradiction right there.
I guess at 19, your highschool didn't teach basics of mathematical analysis.
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Anonymous2006-08-07 14:19
>>23 Furthermore, in practical math such small no's as 0.000...1 are irrelevant and considered 0.
*sigh* It's not a matter of practicality, it's that "0.00...(infinite zeroes)...1" is not a number in the first place. That expression just doesn't make any fucking sense.
God damnit it pisses me off how people think mathematics is some vague, sloppy thing where we just write away things like this for convenience. Mathematics is the most rigorous and well-defined field of academia in existance, and yet here comes Anonymous outsmarting the greatest scientific minds of the past two thousand years.
Just get the fuck out with your 0.999...=1 threads. GTFO.
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Anonymous2006-08-07 14:27
IS DIAMOND * 1.000...1 A METAL?
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Anonymous2006-08-07 16:06
use periods, not commas, eurotrash!
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Anonymous2006-08-07 20:19
>>23
5-(0.4 + SUM[N=1 to infinity]( 0.9/(10*N) ) = 0
There's no such number as 0.00..infinite 0s...1
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Anonymous2006-08-07 21:09
>>19 You just need to understand that 0.0...1 is so small that in reality it is 0.
NO. 0.0...1 IS NOT A NUMBER. THERE IS NO FUCKING APPROXIMATION INVOLVED.
for some reason i feel like my expression and yours are not the same but it is late and i probably forgot something essential
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Anonymous2006-08-08 1:39
>>30
You don't need the limit, you just need to know how to sum infinite geometric series.
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Anonymous2006-08-08 6:27
what is 0.5-0.49999999..=? 0? In math really small no's like the supposed one: 0.0...1 are so small and insignificant that they are 0. Its like this, since there already are an infinite no. of 0's before the 1 the no. is in fact 0. But arguing that: 5=4.99... thus 5-4.999...=0.0...1=0 but 0.0...1=!=0 is retarded! the two arguments are identical.we learnt this in like 2nd or 3rd year math. so gtfo with your go back to school comments and suck my professors balls.
Its 'cos of dipshits like you that wikipedia is and always will be worse than good encyclopedia's.
1.999... is infinitely close to 2, so it is equal to 2. Also, 1.999... is not a real number since it involves the limit as the number of 9s approach infinity.
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.