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x + y = x, solve for X (pg. 7)
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| drizzt81 |
| quote: | Originally posted by Nadi
and drizzt your solving for y not x :eek: |
because the equation is only true if and only if y = 0
if y = 0, then x is element of the real numbers. |
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| Resnick |
| quote: | Originally posted by mezzir
thread of the week!
btw we need more simple problems to overanalyze
ooh wait nm, i got it
.99999(repeating) = 1
discuss. |
hmmm well this isnt true so...i dunno what u guys are proving ^^^ |
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| DrUg_Tit0 |
| quote: | Originally posted by Resnick
hmmm well this isnt true so...i dunno what u guys are proving ^^^ |
It is if the number of repeating is infinite. Because 1-0.999... is then an infinitely small amount, or zero in other words. |
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| whiskers |
| quote: | Originally posted by Lover Boy
Antidifferentiate eh? I'm quite sure that's called Integration m8 ;) & if u differentiated then integrated a fucnction you'd arrive back at the original function. So ull b sellin the exact same song 2 ppl. Or wos that ur point? |
you're mistaken, i will sell teh derivatives of songs and also their antiderivatives, aka f'(x) and F(x)
antidifferentiation = finding antiderivatives of functions
integration = finding area, unless you're doing an indefinite integral |
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| Resnick |
| quote: | Originally posted by DrUg_Tit0
It is if the number of repeating is infinite. Because 1-0.999... is then an infinitely small amount, or zero in other words. |
first of all infinite isnt a number, and no its not, .9999 will never reach 1 if u keep adding 9's
heres an exercie, start writing .9 and keep adding 9's, tell me when u get to 1 :) |
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| whiskers |
| quote: | Originally posted by DrUg_Tit0
It is if the number of repeating is infinite. Because 1-0.999... is then an infinitely small amount, or zero in other words. |
i tend to disagree
1-0.99999.... is an infinitely small amount, but it IS NOT zero |
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| Resnick |
| quote: | Originally posted by whiskers
i tend to disagree
1-0.99999.... is an infinitely small amount, but it IS NOT zero |
ya exactly
the only way u can say .9999 = 1 is by saying the limit of adding inf 9's = 1...
but thats limit, and has nothing to do with the actual value |
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| MK-S |
| quote: | Originally posted by Resnick
first of all infinite isnt a number, and no its not, .9999 will never reach 1 if u keep adding 9's
heres an exercie, start writing .9 and keep adding 9's, tell me when u get to 1 :) |
The fact that it effectively has an infinite number of decimal places means it tends to 1, and is mathematically excepeted as 1, as far as I know. |
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| Smeagol |
well, that's what differs infinity from large numbers, with infinite amount of decimals you'll actually reach the limit.
0.9999... cannot be interpreted in any other way than the limit of the sequence 0.9, 0.99, 0.999, ....
which is one, as earlier proved. :)
I would prefer the primitive rather than the derivative.
A LOT more bass! :) |
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| whiskers |
| quote: | Originally posted by Smeagol
0.9999... cannot be interpreted in any other way than the limit of the sequence 0.9, 0.99, 0.999, ....
which is one, as earlier proved. :)
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yes, but once again, people seem to get confused about the fact that 1 is the LIMIT, not the sequence itself.
the sequence never equals one, it's infinite
it's just that people have a problem with infinity - we cannot grasp it. we imagine it as something really large, but in fact, no matter how large we imagine the infinity to be, the infinity will always be an infinite times bigger then what we imagine it to be, because it's infinite!
there are even different sizes of infinity, but does one infinity ever equal the other?
http://www.math.uiuc.edu/~mileti/Museum/infinite.html
http://en.wikipedia.org/wiki/Infinite |
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| DrUg_Tit0 |
| quote: | Originally posted by Resnick
first of all infinite isnt a number, and no its not, .9999 will never reach 1 if u keep adding 9's
heres an exercie, start writing .9 and keep adding 9's, tell me when u get to 1 :) |
Never, because I can't write it for an infinite amount of times. And no, infinity isn't a real number, that's exactly why the rules for real numbers don't apply here.
| quote: | Originally posted by whiskers
1-0.99999.... is an infinitely small amount, but it IS NOT zero
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1-0.999...=1-lim(sum(n=0->inf)(0.9*10^-n))=1-1=0 |
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| whiskers |
| quote: | Originally posted by DrUg_Tit0
1-0.999...=1-lim(0.999...)=1-1=0 |
i know you're smart and all, but this time you got it wrong.
1-0.999... = lim (1-0.999999999999999999999.....) = lim(0.000000000.....0001) = 0
***EDIT: caught you editing :whip: |
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