I see you are trying to represent a real number with a string of characters. However, you have not supplied enough information to allow us to accurately determine which real number you mean.
Please tell us the location of the final 9 in this string:
0.999...9
We expect this to be a natural number. Failure to provide such a position will prevent us from determining your number, and will make the majority of your argument void.
NOW THAT YOU'VE READ THIS MESSAGE, YOU'VE GOT 24 HOURS TO LEARN THE SERBIAN LANGUAGE. IF YOU FAIL, YOU WILL DIE A HORRIBLE DEATH EXACTLY 24 HOURS FROM NOW. НE СEJ ТИКВE ГДE JOШ НИСУ НИКЛE!
Name:
Anonymous2007-05-12 19:32 ID:yFChcQtv
I AM A MATHEMATICIAN AT A PRESTIGIOUS ENGLISH UNIVERSITY, AND I DECLARE THIS PROOF TO BE COMPLETELY CONSISTENT AND CORRECT
>>14
Dude, you know Grothendieck? Fucking awesome! Can you give me his number?
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Anonymous2007-05-13 12:01 ID:6S5Kzpy/
>>1
There is no such number. In fact, these .9... numbers don't even exist. Sure, they can be expressed using summation, but that doesn't mean they exist numerically.
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Anonymous2007-05-13 14:02 ID:NmaKCHb0
.999...
= sum 9/(10^k)
k=1 to inf
= sum 9*(1/10)^k
k=1 to inf
= (sum 9*(1/10)^k) - 9
(k=0 to inf )
The first term is now a geometric series and therefore:
if we let k tend to infinity, we will arrive at an "expression" for 0.999~
however, since k --> infinity => 1/k --> 0 => 1 - 1/k --> 1
0.999~ = 1
LEARN WHAT INFINITY IS, AND THEN GET YOUR HEAD AROUND WHAT 0.999~ ACTUALLY REPRESENTS. I'M SICK OF THIS FUCKING BULLSHIT FROM PEOPLE WHO DON'T BELIEVE IT AND COME UP WITH BULLSHIT "THEOREMS"
Name:
Anonymous2007-05-13 22:10 ID:6S5Kzpy/
.9... isn't a number. Saying something that isn't a number equals a number is ridiculous. Let's move on from this endless nonsense.
>>22
You can post this however many times you want, it doesn't change the fact that you are wrong.
Name:
Anonymous2007-05-14 0:45 ID:2YwYUj/X
>>23
It is correct. Many mathematicians are arrogant, and later on they are rightly proved incorrected. Summation is a process, and it is not necessarily have a real number as its result. If you think it does, name the exact number. But you can't because it is proof by contradiction (no number you can provide equals ".9..." exactly).
Here's an idea: Take a fucking high school calculus class so that you understand why you're wrong in this statement. Then, take a fucking analysis class so that you understand the definition of the real numbers. When you accomplish these two things - and it'll take you a while, since you seem pretty slow - you can come here and discuss whether or not 0.999.. = 1. But of course, if you've actually accomplished these two things, then you won't believe that 0.999... != 1, so it's a bit of a catch 22. (Catch 21.999... lolol)
Everyone who has posted here knows that .999... == 1. The people who are 'wrong' on this thread are acting that way intentionally. I imagine half of the people who correct them to know this, the other half thinks the 'wrong' people are just wrong. And the only people that believe .9999... != 1 are too busy laughing at us.
Name:
Anonymous2007-05-14 14:36 ID:zCqfq85R
here:
let X = 1 + 3 + 9 + 27 + ...
then 3X = 3 + 9 + 27 + 81 + ...
and X - 3X = 1 (by cancellation). So 2x = 1 or X = 0.5 HOW
>>35
You can't operate on non-convergent series and expect to get a correct answer. I'm not sure if you're the same idiot as before, so this might be redundant, but: learn high school calculus.
Name:
Anonymous2007-05-14 17:03 ID:2YwYUj/X
>>32
I've taken these classes and got decent grades in them. You get bent out of shape when you are asked to provide something and can't do it. Reeks of phailure to me.