## Search found 48 matches

- Sun Jul 28, 2013 9:18 pm UTC
- Forum: Mathematics
- Topic: Dirichlet's theorem on arithmetic progressions
- Replies:
**6** - Views:
**2650**

### Re: Dirichlet's theorem on arithmetic progressions

we'd see that mod 3 is independent of mod 5, but this is given that they are uniformly distibuted arounds those 8 residuals. Is this so? According to Wikipedia, yes. A quantitative form of Dirichlet's theorem states that if N≥2 is an integer and a is coprime to N, then the proportion of the primes ...

- Sun Jul 28, 2013 12:58 am UTC
- Forum: Mathematics
- Topic: Dirichlet's theorem on arithmetic progressions
- Replies:
**6** - Views:
**2650**

### Re: Dirichlet's theorem on arithmetic progressions

But 15 is not a prime. I'm talking specifically of mod p (where p is prime). Sorry if I wasn't clear on that. Or did you mean something else? A prime number (not counting 3 or 5) could only be either 1,2,4,7,8,11,13,14 in mod 15. So if they are uniformly distributed around those residuals (all occur...

- Sat Jul 27, 2013 11:59 pm UTC
- Forum: Mathematics
- Topic: Dirichlet's theorem on arithmetic progressions
- Replies:
**6** - Views:
**2650**

### Dirichlet's theorem on arithmetic progressions

Heya, I was just wondering if somebody here could tell me if Dirichlet's theorem on arithmetic progressions is true for intersections of modulo for several primes. An example. As I understand it, Dirichlet's prime theorem will state that all prime numbers will be either 1 or 2 in mod 3 with a probab...

- Wed May 16, 2012 9:14 pm UTC
- Forum: Logic Puzzles
- Topic: Betting Paradox
- Replies:
**23** - Views:
**7248**

### Re: Betting Paradox

Ah. Thanks for the link. So I guess that resolves it.

- Wed May 16, 2012 8:59 pm UTC
- Forum: Logic Puzzles
- Topic: Betting Paradox
- Replies:
**23** - Views:
**7248**

### Re: Betting Paradox

While that is true, probability theory also says (unless I've missed something) that any event with a probability greater than 0, if repeated infinite times, will happen. Since not losing a game = 50%, winning x times in a row = (1/2)^x. If x goes to infinity the probability of not losing goes to ze...

- Wed May 16, 2012 7:14 pm UTC
- Forum: Logic Puzzles
- Topic: Betting Paradox
- Replies:
**23** - Views:
**7248**

### Re: Betting Paradox

Well, personal assumpsions/values can allow you to do anything (thus beating any action paradox). But if dollars are valued equally at all times (i.e no decreasing marginal utility), then I'd assume that one would always play the game, thus playing unlimited amount of times. But the expected value o...

- Wed May 16, 2012 4:53 pm UTC
- Forum: Logic Puzzles
- Topic: Betting Paradox
- Replies:
**23** - Views:
**7248**

### Betting Paradox

Don't know if this is supposed to go into the Mathematics section since it's more of a paradox than a puzzle, but I think it applies to this area. This is a version of the dubble down betting policy (i.e. in a fair double or nothing game you bet double the amount you perviously bet if you lost that ...

- Sun Sep 25, 2011 11:57 pm UTC
- Forum: Books
- Topic: Books you like that no one else has heard of
- Replies:
**88** - Views:
**20846**

### Re: Books you like that no one else has heard of

My 2 cents: * Didn't like "Sophie's World" - I liked far more " Plato and a platypus... " * Jonathan Strange & Mr Norrel - did enjoy it, but won't read it a second time Now something from my own collection that nobody I know has ever heard about: * The detective novels on Ju...

- Sun Sep 25, 2011 11:19 pm UTC
- Forum: Books
- Topic: Recommend me a good short story author...
- Replies:
**48** - Views:
**66027**

### Re: Recommend me a good short story author...

If by short you mean short and by good, you mean witty dialogue consisting of comebacks on par with Oscar Wilde, then I recommend Saki (Munroe). Especially his stories about Reginald. Amazing. You can buy them for a pittance at amazon, or any book store / book dealer, or read them for free online.

- Sun Sep 25, 2011 9:43 pm UTC
- Forum: Books
- Topic: Books you had to read for school that you could not stand
- Replies:
**778** - Views:
**212377**

### Re: Books you had to read for school that you could not stan

Jane Eyre was sorta meh, same goes for The Scarlett Letter and Lord of the Flies. My hatred is reserved for Toni Morrison's "The Bluest Eye". It just seemed to arbitrary, too pc in a wannabe non-pc obnoxious way. Bah, no thank you. Thank fully I also got to read a whole lot of amazing book...

- Sun Sep 25, 2011 9:30 pm UTC
- Forum: Books
- Topic: xkcd's favourite 100 books - vote now!
- Replies:
**226** - Views:
**185744**

### Re: xkcd's favourite 100 books - vote now!

Personal top 5 plus two late contenders:

The Black Book by Orhan Pamuk

Steppenwolf by Herman Hesse

The Ink Drum by Günter Grass

The Master and Margarita by Mikhail Bulgakov

Cancer Ward by Aleksandr Solzhenitsyn

I Am a Cat by Natsume Soseki

We by Yevgeny Zamyatin

The Black Book by Orhan Pamuk

Steppenwolf by Herman Hesse

The Ink Drum by Günter Grass

The Master and Margarita by Mikhail Bulgakov

Cancer Ward by Aleksandr Solzhenitsyn

I Am a Cat by Natsume Soseki

We by Yevgeny Zamyatin

- Sun Sep 25, 2011 9:08 pm UTC
- Forum: Logic Puzzles
- Topic: Looking for hard and rare logic puzzles
- Replies:
**60** - Views:
**20792**

### Re: Looking for hard and rare logic puzzles

Ok, I think I understand. So what distribution does it follow, or what distributions/biases can we restrict it to? I've read the posts above but to me they're a tad difficult to follow. What would be the layman's answer of the strategy that benefits from the potential bias (or most potentials biases)?

- Sun Sep 25, 2011 8:48 pm UTC
- Forum: Mathematics
- Topic: The Flaws of Mathematics as a Universal Language
- Replies:
**22** - Views:
**4072**

### Re: The Flaws of Mathematics as a Universal Language

Considering that we invented counting long before we invented logic, I don't know why that would have to be the case. But isn't the logic "invented" by the greeks, etc a formalization of conventional, structured thinking. Economics wasn't invented until late in history. That doesn't mean ...

- Sun Sep 25, 2011 8:44 pm UTC
- Forum: Logic Puzzles
- Topic: Looking for hard and rare logic puzzles
- Replies:
**60** - Views:
**20792**

### Re: Looking for hard and rare logic puzzles

This is one of those slightly weird facts. There isn't any way to choose real numbers in a uniform way. It would require that the probability of picking a number between 0 and 1 was the same as picking between x and x+1 for all real numbers x. Isn't it? I thought the probability of picking a number...

- Sun Sep 25, 2011 8:42 pm UTC
- Forum: Mathematics
- Topic: The Flaws of Mathematics as a Universal Language
- Replies:
**22** - Views:
**4072**

### Re: The Flaws of Mathematics as a Universal Language

Wouldn't a system of counting similar to ours depend on a system of logic similar to ours? Or am I missing something?

- Sun Sep 25, 2011 8:27 pm UTC
- Forum: Mathematics
- Topic: Should we make students memorize the quadratic formula?
- Replies:
**61** - Views:
**9039**

### Re: Should we make students memorize the quadratic formula?

I see it as similar to memorizing multiplication tables or tables of basic integrals or the mean and variance of common distributions. Sure, it's possible to compute all those things from first principles every time, but whenever you actually have to use it, you're probably not going to have time t...

- Sun Sep 25, 2011 8:11 pm UTC
- Forum: Logic Puzzles
- Topic: Looking for hard and rare logic puzzles
- Replies:
**60** - Views:
**20792**

### Re: Looking for hard and rare logic puzzles

Aren't there and equal amount of real numbers above zero as below zero? You have no idea how the numbers are chosen, hence you cannot assume certain numbers are favoured higher than others. Hence an equal (uniform) distribution of all numbers. So if your number is a number below zero th...

- Sun Sep 25, 2011 8:07 pm UTC
- Forum: Logic Puzzles
- Topic: Monty Hall Problem [solution discussion]
- Replies:
**68** - Views:
**26128**

### Re: Monty Hall Problem [solution discussion]

If I were willing to bet you a dollar against a dollar for any team against any other team in any MLB or NFL game, you would do well to take my bet, and just adopt a simpleminded strategy such as "Always pick the team with the better record." In the long run, you will win money. In practi...

- Sun Sep 25, 2011 8:02 pm UTC
- Forum: Mathematics
- Topic: Should we make students memorize the quadratic formula?
- Replies:
**61** - Views:
**9039**

### Re: Should we make students memorize the quadratic formula?

Why memorize it? I mean, sure if you want to, but if you know completing the square you can always derive it by completing x^2+ax+b = 0 (switch a and b for p and q, etc). I know it sorta, but I can always get it if I need it, the same goes for the quotient rule when doing derivativies. If you can de...

- Sun Sep 25, 2011 7:56 pm UTC
- Forum: Mathematics
- Topic: The Flaws of Mathematics as a Universal Language
- Replies:
**22** - Views:
**4072**

### Re: The Flaws of Mathematics as a Universal Language

Hubble is a technological invention, which we ourselves will (hopefully) one day find quaint. And sure, it *might* be possible for an alien race to have fundamentally different mathematics, though even that possibility is not certain. But surely you admit that mathematics could be a more universal ...

- Wed Sep 14, 2011 3:46 pm UTC
- Forum: Logic Puzzles
- Topic: Looking for hard and rare logic puzzles
- Replies:
**60** - Views:
**20792**

### Re: Looking for hard and rare logic puzzles

Well, there was one that made the xkcd newsblag a while back: You are presented with two indistinguishable envelopes and allowed to choose one. Each envelope contains a real number, and the numbers are different. You open your envelope and see the number inside. Now you must guess whether the numbe...

- Wed Sep 14, 2011 11:56 am UTC
- Forum: Logic Puzzles
- Topic: Monty Hall Problem [solution discussion]
- Replies:
**68** - Views:
**26128**

### Re: Monty Hall Problem [solution discussion]

This is the heart of the problem: Much like a lotto ticket isn't changing as I'm scratching it; the car isn't jumping around behind the doors and I'm not magically half-guessing a different door. Once a choice has been made *that trial* is subject to the choice that was made and cannot be changed. ...

- Wed Mar 30, 2011 1:03 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0879: "Lamp"
- Replies:
**151** - Views:
**37282**

- Mon Feb 14, 2011 6:28 pm UTC
- Forum: Mathematics
- Topic: Question about large prime numbers
- Replies:
**6** - Views:
**1590**

### Re: Question about large prime numbers

Thanks for the quick reply. There are a couple of different ways. The largest known prime numbers are generally Mersenne primes , primes of the form 2 p -1 for some number p. You can show that if 2 p -1 is prime, then p is also prime (but not vice versa). The current record primes have p at around 8...

- Mon Feb 14, 2011 4:54 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0860: "Never Do This"
- Replies:
**110** - Views:
**53290**

### Re: 0860: "Never Do This"

Is this whole "being completely disgusted by normal bodily functions" an American thing? I bet it's all the marketing. After all, what better way to sell a new kind of cleaning product than convincing the populace that some innocuous thing they've never given a second thought is the gross...

- Mon Feb 14, 2011 4:35 pm UTC
- Forum: Mathematics
- Topic: Question about large prime numbers
- Replies:
**6** - Views:
**1590**

### Question about large prime numbers

Hi, I did a search but couldn't find anything close to my question. Googling it didn't help much either. Basically what I'm wondering is how do people find large primes. Do they look at every number to check if it's a prime (or skip some easy ones like divisible by 2 or 3 or 5), or are there more ad...

- Thu Feb 03, 2011 2:40 am UTC
- Forum: Logic Puzzles
- Topic: Twins in a Maze
- Replies:
**81** - Views:
**21928**

### Re: Twins in a Maze

Adacore wrote:Superisis:Spoiler:

It said in the original post that time was not a factor.

- Tue Feb 01, 2011 3:05 pm UTC
- Forum: Logic Puzzles
- Topic: Twins in a Maze
- Replies:
**81** - Views:
**21928**

### Re: Twins in a Maze

Yeah, I think that's right: Obviously if you can come up with any way to differentiate the twins, the problem becomes trivial - one twin just has to stand there while the other performs a comprehensive search. Again, with randomness the probability rapidly approaches (although can never be exac...

- Tue Feb 01, 2011 2:44 pm UTC
- Forum: Mathematics
- Topic: Probability (chances of winning a game)
- Replies:
**6** - Views:
**1282**

### Re: Probability Problem

Isn't this the same intuition as the birthday paradox. Ie, you need not many people in a group for two to share a birthday (which is counter intuitive). I guess people think (intuitively) that results are more evenly spread out than they actually are.

- Tue Feb 01, 2011 2:37 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0854: "Learning to Cook"
- Replies:
**134** - Views:
**25886**

### Re: 0854: "Learning to Cook"

For all of you who say cooking is too hard/too expensive/requires too many ingredients/takes too much time from Starcraft 2 I've got one word:

Dal.

Dal.

- Tue Jan 25, 2011 11:35 am UTC
- Forum: General
- Topic: xkcd is a "legendary" site, according to Mensa
- Replies:
**61** - Views:
**8762**

### Re: xkcd is a "legendary" site, according to Mensa

Hear, hear! Specially if you've taken a standardized, off the line, IQ-test (and not been individually evaluated). In my opinion these tests (which mensa uses to screen applicants) are not true tests of intelligence (of the top 2%) but tests of information and above average intelligence. And as we ...

- Tue Jan 25, 2011 10:46 am UTC
- Forum: General
- Topic: xkcd is a "legendary" site, according to Mensa
- Replies:
**61** - Views:
**8762**

### Re: xkcd is a "legendary" site, according to Mensa

I'm not sure about my IQ rating. I do tend to catch on to things very quickly, though. Honestly, the most hilarious thing about IQ is that you are much better off NOT knowing your IQ than you are knowing it. If you know it, there's a chance you'll develop a tendency to unconciously limit yourself. ...

- Mon Jan 24, 2011 8:05 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0850: "World According To Americans"
- Replies:
**712** - Views:
**176419**

### Re: 0850: "World According To Americans"

Fat Tony wrote:Not that any of this is relevant, but it seemed like we were in the mood for pedantry. I just wanted to be cool like all you guys =D

Hey. Non ti preoccupati, sei cool!

I, had a post here about 2D map but it turned out I was wrong... so I'll have to go back to MS paint I guess

- Sun Jan 23, 2011 10:18 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0850: "World According To Americans"
- Replies:
**712** - Views:
**176419**

### Re: 0850: "World According To Americans"

Conveniently, I'm relatively competent at geography, but I still defend the Americans who can't tell you where Latonia is because the location of Latonia on a map has nothing to do with our day-to-day lives. I can agree that Latonia has little to do with our daily lives, but I assume you where refe...

- Sat Jan 22, 2011 10:46 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0850: "World According To Americans"
- Replies:
**712** - Views:
**176419**

### Re: 0850: "World According To Americans"

So you're saying people who live in Tennessee have no unique culture nor history worth knowing? Who's the one being ethnocentric now? Everyone, everywhere has a unique culture and history. You cannot argue that one is more worth knowing than another simply because its distribution happens to coinci...

- Fri Jan 21, 2011 10:06 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0850: "World According To Americans"
- Replies:
**712** - Views:
**176419**

### Re: 0850: "World According To Americans"

If you expect someone from the U.S. to know where, say, Finland is, I think he's pretty justified in expecting you to know where Tennessee is, considering it has a larger population and GDP than Finland. People expect you to know where Finland is because of culture and history, not because of how m...

- Fri Jan 21, 2011 9:43 pm UTC
- Forum: Logic Puzzles
- Topic: Prisoners Problem (Easy Mode)
- Replies:
**17** - Views:
**5766**

### Re: Prisoners Problem (Easy Mode)

[ Edit: Dang, I just came up with another possibility. ] Since there is no down-side given to providing a wrong answer, the third prisoner thinks about the fact that there are a total of three white hats and two black hats, reasons that this means that there is a 3/5 (60%) chance of his hat being w...

- Fri Jan 21, 2011 9:27 pm UTC
- Forum: Logic Puzzles
- Topic: Playing Magic (or Poker, whatever)
- Replies:
**11** - Views:
**3353**

### Re: Playing Magic (or Poker, whatever)

For at-least and at-most 3 cards, we sum up the number of ways to make a hand with 0, 1, 2, and 3 (or 3, 4, 5, 6, and 7) before dividing. To calculate these, change the 3 in 17C3 and the 4 in 23C4 to the number, and 7 - the number. A faster was to calculate at-most 3 cards is to calculate at-least ...

- Fri Jan 21, 2011 6:31 pm UTC
- Forum: Mathematics
- Topic: Useless Math
- Replies:
**60** - Views:
**10366**

### Re: Useless Math

The problem is that if you're building you proof on " maths is not inherently connected to the real world and any connection we find is accidental because look this, this, and this discovery is completely useless " you will have all the examples (mentioned previously by others) of apparent...

- Fri Jan 21, 2011 12:57 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0850: "World According To Americans"
- Replies:
**712** - Views:
**176419**

### Re: 0850: "World According To Americans"

You raise a fair point that countries in Europe should be compared to states of the US. Although that's not entirely fair either, since Europe has fewer nations than the US has states, and twice the population. Also most Europeans do not know all the tiny countries (Andorra, Liechtenstein, Monaco, ...