>>2
That's a horrid proof, but yes, as everyone else said, it does.
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Anonymous2005-11-16 10:48
IT DOESN'T NEED PROOF. IT'S LIKE THAT BY DEFINITION YOU FUCKING IDIOTS.
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Anonymous2005-11-16 12:40
if it's like that by definition then it doesn't have a proof
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Anonymous2005-11-16 15:20
>>8
Nothing in mathematics is like something by definition. Everything in mathematics can be proven (or disproven).
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Anonymous2005-11-16 16:11
>>10
no. the + function is defined. sqrt, *, / ... the list goes on. you have to define some things to contruct other things and prove other things assuming the definitions.
key word is assume here. ex: if we assume the derivative of ln(x) = 1/x, then we can prove that the derivative of e^x is e^x.
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Anonymous2005-11-16 17:35
Actually, that would be "if we assume the derivative of f(x), f'(x), is the slope of f(x) at every value x, then the derivative of e^x is e^x."
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Anonymous2005-11-16 18:58
Saying that .9~=1 is like saying that 9=10. You're ignoring basics of math. You can't distort equations to prove your ignorance.
Different values cannot be equal! .9~ and 1 are different. As the linked forum topic says: Infinity DOES NOT EXIST- it's just an abstract word.
Therefore, if infinity does not exist, .9~ actually means .9..9 And that isn't one. That's .9...9. It's a matter of believing and infinity and not. You're probably just a bunch of Christian fundamentalist engineers with too much time on your hands who want to distort your own knowledge to prove God.
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Anonymous2005-11-16 19:42
Infinity does exist; it's just a concept. Similarly, thoughts exist, but not physically.
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Anonymous2005-11-16 19:44
.9(...)9 is equal to 1 in a "real life" sense, even though .9(...)9 is actually infintesimally smaller than 1.
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Anonymous2005-11-16 19:49
For all purposed .999...9 might as well be 1. So it should be defined to be 1. Unless it's inconvenient lol.
if you believe that every subset of the natural numbers has a least element, then you are forced to discard the concept of an infinintesimally small number.
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Anonymous2005-11-16 22:11
maybe you could think of 1-.9999... as 1/infinity or lim(x->inf, 1/x)
You've made us all stupider. Read the massive quantities of explanation linked to by >>6 before sharing any further idiocy. .9 repeating is not, and never will be, .9..9.
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Anonymous2005-11-16 23:38
the thread in >>6 is unreadable. what's with all the [smiley.gif] crap? someone should link to a nice readable proof or some math fag saying it's defined or something.
Your second assertion, that .9 repeating and 1 are different simply because they look different, is patently silly. A single number has an infinite number of representations. 2/6 is the same number as 1/3, even though the look different. .9 repeating is simply another name for 1. The numbers exist independent of our representation of them.
the notation is part of a mental effort of >>15 to cling to the concept of the infinintesimal. What is implied is that you could add 0.0000....00001 (infinitely many zeroes) to .9(...)9 in order to get one. What is further implied, or desired, is that performing this particular sum is somehow distinct from adding 0 to 1, when in fact it is not.
The interesting thing is that such a number as .9(...)9, if it even exists, doesn't belong to the set of reals. While .9... (where .9... is .9 repeating) most certainly does. >>15,>>25 should read >>6's link more thoroughly. This is discussed there in great detail.
>>15,>>25
There is no "infinitesimal" difference between .9... and 1. Check the linked post for Icarus' Misconception 8 (That "There is a least number greater than or greatest number less than a given real number.") Your view seems to be centered on this misconception. 0.9... is not, and cannot be, the "greatest number that's less than" 1.
it's real. why wouldn't it be real? just as .9, .99, .999 are improving approximations of .9..., .99, .999, .9999, are improving approximations of .9(...)9. In fact, you could write .9(...)169328472169894823 where ... represents another infinite string of nines, and IT ALL EQUALS ONE.
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dv2005-11-17 9:22
OMG YOU SHITS
1) REAL NUMBERS ARE THE CLOSURE (SEE BASIC TOPOLOGY) OF RATIONAL NUMBERS.
2) ALL CAUCHY SEQUENCES IN THE REAL NUMBERS CONVERGE TO A _UNIQUE_ REAL NUMBER
3) THE SEQUENCES 1,0,0,...,0 and 0,9,9,...,9 CONVERGE TO THE SAME FUCKING REAL NUMBER (LIM(N->INF, 1) = 1, AND LIM(N->INF, 1-(1/10^N)) = 1)
HENCE THEY ARE THE SAME FUCKING NUMBER
QUOD ERAT DEMONSTRANDUM
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dv2005-11-17 9:27
LOL OOPS. I MEANT COMPLETION NOT CLOSURE. I SUCK COCK
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Anonymous2005-11-17 9:32
ERRATA #2 (whoa dude, this is turning out like a Rudin book): I MEANT THE SEQUENCES OF APPROXIMATIONS 1.0, 1.00, 1.000, ... AND 0.9, 0.99, 0.999, ... CONVERGE TO THE SAME REAL NUMBER
doh'
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Anonymous2005-11-17 10:52
>>30
Yes there is, .9 repeating is infintesimally smaller than 1. However, for every day use it can equal 1 because, well, no one really uses infintesimals in their day-to-day lives outside of work.
Shut up until you understand decimal representations of real numbers, because currently you clearly don't. Refer to Misconceptions 1 ("Infinite Decimals are Approximations"), 7 ("There are numbers without decimal representations"), and 8 ("There is a least number greater than or greatest number less than a given real number") in >>6's link because you seem to be falling afoul of them with your statement of decimals being "inaccurate".
And consider yourself bitchslapped per >>36's request.