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.