Glory ,'The Killer In Me'
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.
t, I'm stuck on (well, I'm stuck on 5 out of 8 of the questions, but the first is):
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)
What was the Poe (I think) story where the guy kills someone, and then becomes obsessed wiping his fingerprints off every object in the house?
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?
In case there was any doubt, the Miami Dolphins suck.
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.
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.
I don't see how it could be anything but what -t said. Unless I'm missing something....
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)
I don't think I can prove it.
Can you assume it's not true, and then show that assumption results in a contradiction?
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.