At least there was guilt! Surprise! Being caught!
Yes, but in my opinion the main thrust of the story was more atmosphere than plotline. What happens in the Raven? There's a bird which for some reason reminds him of his dead girlfriend, the end?
Jayne: Yeah, that was some pretty risky sittin' you did there. Wash: That's right, of course, 'cause they wouldn't arrest me if we got boarded, I'm just the pilot. I can always say I was flying the ship by accident.
'Serenity'
Natter 40: The Nice One
Off-topic discussion. Wanna talk about corsets, duct tape, or physics? This is the place. Detailed discussion of any current-season TV must be whitefonted.
Emily - Dec 04, 2005 8:13:07 am PST #9183 of 10006
"In the equation E = mc⬧, c⬧ is a pretty big honking number." - Scola
Laura - Dec 04, 2005 8:16:53 am PST #9184 of 10006
Our wings are not tired.
In case there was any doubt, the Miami Dolphins suck.
-t - Dec 04, 2005 8:21:28 am PST #9185 of 10006
I am a woman of various inclinations and only some of the time are they to burn everything down in frustration
Oh dear, that sounds like something I used to be able to do. Sorry, Emily, I am no help whatsoever.
Okay, wait, finitely many sixes after the decimal, so the least upper bound would probably be 2/3, because for any .66...6 with n-many 6s you can always just add another 6 on the end and get a higher member of the set. And if you mix 0s in there, it'll get lower.
No, that's probably still no help.
I think that the reader was supposed to be surprised by the walling up, it's just that we all know the story now.
Emily - Dec 04, 2005 8:24:39 am PST #9186 of 10006
"In the equation E = mc⬧, c⬧ is a pretty big honking number." - Scola
Okay, wait, finitely many sixes after the decimal, so the least upper bound would probably be 2/3, because for any .66...6 with n-many 6s you can always just add another 6 on the end and get a higher member of the set. And if you mix 0s in there, it'll get lower.
I suppose that's true. I guess I'm just confused by the use of "least upper bound" here. I mean, there's no number such that all numbers smaller than it in the interval are like that, except 3/5, and that doesn't seem to be the meaning.
tommyrot - Dec 04, 2005 8:26:05 am PST #9187 of 10006
Sir, it's not an offence to let your cat eat your bacon. Okay? And we don't arrest cats, I'm very sorry.
I don't see how it could be anything but what -t said. Unless I'm missing something....
-t - Dec 04, 2005 8:31:15 am PST #9188 of 10006
I am a woman of various inclinations and only some of the time are they to burn everything down in frustration
Ganked from [link]
The least upper bound, called the supremum, of a set S, is defined as a quantity M such that no member of the set exceeds M, but if ? is any positive quantity, however small, there is a member that exceeds M - ?.
I think it's 2/3. I don't think I can prove it.
(The ?s are epsilons)
tommyrot - Dec 04, 2005 8:32:43 am PST #9189 of 10006
Sir, it's not an offence to let your cat eat your bacon. Okay? And we don't arrest cats, I'm very sorry.
I don't think I can prove it.
Can you assume it's not true, and then show that assumption results in a contradiction?
-t - Dec 04, 2005 8:35:41 am PST #9190 of 10006
I am a woman of various inclinations and only some of the time are they to burn everything down in frustration
I think all that needs to be shown is that for any positive x, there exists a member of the described set between 2/3-x and 2/3. The proof is left as an exercise for the reader.
Emily - Dec 04, 2005 8:36:46 am PST #9191 of 10006
"In the equation E = mc⬧, c⬧ is a pretty big honking number." - Scola
Oh, okay. Using that definition, I think it does work. I was looking at
If a property M does not belong to all values of a variable x, but does belong to all values which are less than a certain u, then there is always a quantity U which is the greatest of those of which it can be asserted that all smaller x have property M
and not getting it. Although now I look at it... I guess it does say the same thing. It was that "a variable x" that was confusing me. Thanks, guys! Now I have to attack Dedekind cuts and paradoxes. My brain really isn't up to this stuff.
Eddie - Dec 04, 2005 8:40:47 am PST #9192 of 10006
Your tag here.
Let A be the set of numbers in (3/5,2/3) that have decimal expansions containing only finitely many zeros and sixes after the decimal point and no other integer. Find the least upper bound of A. (prove your answer)
My head hurts, and I can't help but wonder what is the practical value of the question. Good luck.