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Old 03-19-2014, 03:38 PM   #13246
pdurrant
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Quote:
Originally Posted by Bilbo1967 View Post
First = eight?
Last = two?

Do you get infinity if you add them all up? Because there are an infinite number of positive integers?
Yes to both. And yes, one answer is that the sum is infinite. It's certainly divergent. But see below.

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most common T
least common O ?
Yes! And all because of ten! Although there's another argument that since there are an infinite number of numbers beginning O, N, F, S and T they are all equally common. However, I was thinking of the answers you gave.

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What's the last number in the list? There isn't one. As Bilbo notes there are an infinite number of positive integers.

Not sure what add them all up would mean either. Eight + ? + T + O = ?
There are an infinite number of numbers in the list, but we can show that the last one is two by asking for a counter-example. There's no number that would come after two, so two must be the last one.


There are some branches of mathematics that try to deal with divergent series. In a very specific mathematical sense, the sum of all the positive integers is negative one twelfth. (-1/12). I confess I don't really understand that myself. Mathematics involving integers is tricky or even tricksy.

I award the win to Bilbo1967. Over to you, Bilbo.
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Old 03-19-2014, 03:55 PM   #13247
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In a very specific mathematical sense, the sum of all the positive integers is negative one twelfth. (-1/12).
That's the kind of thing that gets mathematics a bad name

Back shortly with some questions.
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Old 03-20-2014, 07:28 AM   #13248
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Yes! And all because of ten! Although there's another argument that since there are an infinite number of numbers beginning O, N, F, S and T they are all equally common. However, I was thinking of the answers you gave.
That is what I was thinking of after my first post. The sets of all positive integers that begin with O, N, F, S, and T are all infinite sub-sets of the infinite set of all positive integers [otherwise known as the natural numbers]. All of these infinite sets are aleph number zero though, so in a sense are all of the same size.



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Originally Posted by pdurrant View Post
There are some branches of mathematics that try to deal with divergent series. In a very specific mathematical sense, the sum of all the positive integers is negative one twelfth. (-1/12). I confess I don't really understand that myself. Mathematics involving integers is tricky or even tricksy.
1+ 2 +3 + . . . some how sums to -1/12? Would you happen to have a link to that?
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Old 03-21-2014, 11:49 AM   #13249
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1+ 2 +3 + . . . some how sums to -1/12? Would you happen to have a link to that?
http://en.wikipedia.org/wiki/Ramanujan_summation

Ramanujan Summation is a way to get a value for a divergent series, in a way that produces the 'correct' answer when applied to convergent series. At least, I think that's what it's doing. It not really a sum in terms of adding things up.
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Old 03-21-2014, 12:04 PM   #13250
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http://en.wikipedia.org/wiki/Ramanujan_summation

Ramanujan Summation is a way to get a value for a divergent series, in a way that produces the 'correct' answer when applied to convergent series. At least, I think that's what it's doing. It not really a sum in terms of adding things up.

it's been years since I have read through a page of text with so many math formulas with subscripts, superscripts, and Greek letters. There were an awful lot of "assumed"s in there as well.

The story of Ramanujan is fascinating. The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel is on my TBR list.
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Old 03-21-2014, 02:48 PM   #13251
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quiz??
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Old 03-24-2014, 08:18 AM   #13252
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Apologies for my tardiness. Below are some quotes regarding lateness. For some I will want the person who said it, for some the book it's from, the author and, sometimes, the character;

1. "Come. Come now or you will be late."
"Late? What for?"
"What is your name, human?"
"Dent. Arthur Dent."
"Late as in the late Dentarthurdent. It's a sort of threat, you see. I've never been terribly good at them myself but I'm told they can be terribly effective."
(Author, book and the one unnamed character please)

2. “She was around ten minutes late, as a matter of fact. I didn't give a damn, though. All that crap they have in cartoons in the Saturday Evening Post and all, showing guys on street corners looking sore as hell because their dates are late - that's bunk. If a girl looks swell when she meets you, who gives a damn if she's late? Nobody.”
(Author and book please)

3. "How did it get so late so soon? Its night before its afternoon. December is here before its June. My goodness how the time has flewn. How did it get so late so soon?"
(Author please)

4. "I am invariably late for appointments - sometimes as much as two hours. I've tried to change my ways but the things that make me late are too strong, and too pleasing."
(Person to whom this quote is attributed please)

5. "Better never than late"
(Person to whom this quote is attributed please)
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Old 03-24-2014, 08:29 AM   #13253
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1. The Hitchhiker's Guide to the Galaxy by Douglas Adams. Is the speaker Marvin?

I'll have to think about the others.
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Old 03-24-2014, 08:45 AM   #13254
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1. The Hitchhiker's Guide to the Galaxy by Douglas Adams. Is the speaker Marvin?

I'll have to think about the others.
Yes, it is THGTTG by Adams. Not Marvin though.

2 points.
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Old 03-24-2014, 09:07 AM   #13255
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1. Slartibartfast
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Old 03-24-2014, 09:09 AM   #13256
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1. Slartibartfast
Yes, correct.

Bookpossum 2 pts
pdurrant 1 pt
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Old 03-24-2014, 09:32 AM   #13257
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Reread it a short while ago.
2. J.D. Salinger and "The Catcher in the Rye"

Last edited by Kumabjorn; 03-24-2014 at 09:35 AM.
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Old 03-24-2014, 09:45 AM   #13258
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Reread it a short while ago.
2. J.D. Salinger and "The Catcher in the Rye"
2pts to Kumabjorn.
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Old 03-24-2014, 09:59 AM   #13259
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3. Ogden Nash?
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Old 03-24-2014, 10:52 AM   #13260
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3. Dr Seuss?

4. Mark Twain?
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