Yoruichi-san

Sorry, but I just have to point something out... Bonanova's explanation makes a lot of sense, but I agree with Octopuppy that it seems to be going the opposite direction as Prime's original question... ...and I think the "infinite exponential" thread has aptly demonstrated that going forwards and backwards aren't necessarily the exact same thing...proving that 2 is equal to the convergence for the infinite exponential series of sqrt(2) does not necessarily mean the convergence of the series will always equal 2...it could also equal 4...

Okay, I've thought of an example that will demonstrate this in a way that makes more sense to everyone who is not me ;P: If I'm going to roll a fair die 500 times, I know that there is some probability that I will roll no 6's. That probability is (5/6)^500, which is small, but not 0. After I roll the die, if I end up rolling any 6's, then you would say the probability of me rolling no 6's would be 0. If I roll no 6's in 500 rolls, you would say the probability of me rolling no 6's is 1. So you can't use the data set to predict the probability of me rolling no 6's, because the only two values you can get are 0 and 1. After the event happens and the results are known, probabilities all become 0 or 1. You can look at the data statistically to try to estimate probabilities, but it is not a proof.

Okay, I think you're confusing probability with statistics... Probability is what you use before you have complete knowledge, i.e. at a time before you roll the die or if you only know certain information about the results. Statistics is what you use to analyze the result set, when you have complete knowledge of the result set. You can use statistics to estimate probabilities to within some degree error, but you can't use it to PROVE that the probability is such and such. It's not so obvious when talking about dice rolls, but a good example of the difference is the collapse of the wavefunction in quantum physics... Before you observe the electron, it has a certain probability distribution, i.e. some probability of being in different locations in space. But after you observe the location of the electron, the wavefunction "collapses" into a delta function and the probability becomes 1 where it is. If you observe N electrons in similar circumstances, you can estimate the probability density function, but these results don't prove what the wavefunction is...you have to do that mathematically, with differential equations...my favorites ;P Edit: In short, what I'm trying to say is that you can't use data sets, no matter how large, to prove probabilities, by definition.

Yeah...sorry guys, I really wanted to get this going ...maybe we should just scrap this one and start a new sign-up and make sure the people signed up are willing/able to participate? Edit: And I don't mind ppl who are new to the game and willing to learn...like Ben Law's questions are good...but we just need ppl who actually want to play...

And now that I think about it, all our proofs have been kind of going backwards, based off assuming that the series converges to a certain value, i.e. 2 or 4, but there is no forwards proof of what value the series converges to... And I don't know how well Excel deals with complex numbers...;P

Wow...that's really interesting! I think it may have to do with...

Edit: Made the correct link more obvious...since ppl are trying so hard

Wow...that was a great episode! My favorite part was the look on Peter's face when Sylar...err, Gabriel ;P... hugged him...Priceless And reviving Adam...can't wait to see what comes of that. But the burning question in my mind is... I guess Peter did get the convicts' powers after all...he used that blue fire. And he got Daphne's superspeed too...the list keeps growing...so you have to wonder why he just can't use them efficiently? Well, now that he has Sylar's understanding ability, maybe he'll be able to figure out the optimum strat...;P ...Oh, and I have to say...I so want to play Mafia with Sylar...

Lol...this is TANTALIZING! I was totally reading the problem wrong at first...but now I think I get it... I'm not sure how solid this is...I'm not sure how sound the assumption inf-1=inf is, but...

Nice. To give Woon credit, though, I think he didn't mean a circular hole, it's just that English is not his first language...;P

I think I see what you're saying, but I still don't think we can look at independent variables as "achieving a result". If I suddenly lost count (due to my mind being on another of your problems ;P), and then you asked me "what is the expected number of rolls you have to do to get a 6", I would still say 6. Independent of past rolls, if you ask at any time for the expected number of rolls, it is still the same because they are independent variables. However, if the man bumps his head one night, and the next morning wakes up with amnesia, the expected days he has to go is not 5, it depends on his past actions.

Woon, you are awesome , but if you posted a new riddle every 10 seconds, I don't think the admins would appreciate it...;P

I'm sorry, it's an interesting way of looking at it, but I don't really think the analogy works for me, because the dice rolls are independent variables, whereas achieving part of a result is not. If I try to look at the days as independent, the man walks 1/5 of the total distance on day 1, then the next day the distance he walks is actually 1/4*4/5=1/4 of his remaining distance, i.e. on day 2 he achieves 1/4 his objective (looking at the days as independent). Whereas if I roll the dice one time, the probability of getting a 6 is 1/6 and if I roll the dice a second time the probability of getting a 6 is still 1/6 and on the 100th roll the probability of getting a 6 is still 1/6. Also, the walk is deterministic, not probabilistic, i.e. after 5 days he will have gotten to the end, no matter what (unless he gets eaten by a large jungle cat), but after 6 rolls, the probability of getting a 6 is not 1, it is 1-prob(no 6s)=1-(5/6)^6.

Okay, I guess I'll give a little...Chaplam 13 had partially the correct interpretation for 4...and for 2...well, name-recognition is important in clothing...;P

Lol...there was only one answer...that was me...and I thought it was simple...;P Reminds me of a story I heard about this genius scientist (way smarter than I could ever be)... One day some one asked him the bird flying b/w two trains problem, i.e. there are two trains coming towards each other and a bird that flies back and forth between the two trains. The question is what distance does the bird fly before the trains collide. So this genius scientist thinks about it for a little while and then gives the answer. The guy who asked the question was like "Wow, you figured out really quickly that all you have to do is find the total time the trains are moving and multiply by the speed of the bird. Most people don't realize that, they try to construct an infinite geometric series and find the sum..." And the genius scientist gives the guy a look and is like "but that's exactly what I did!" True story, I heard it from a professor at college. Edit: Added smiley ;P

I have no skill with draw software, so I'll just try to explain where I got this from in words:

Lol...nice!

Thanks, Andromeda, it was great fun! You left out some of my favorites, though...;P Birthed here by descendants of the Middle Kingdom to die Questionable cheating creates hairdos Hunt for Rabbit Blues Brother Fabric blocking out the sun

Aha! Okay, I get the -o now...thought it was suppose to be a gender sign for awhile...;P

No...Sinistral has a Horse -1 which means he sees everyone a distance 1 closer...

He has a Gun 4 so he can shoot anyone he wants...guns allow you to play Shoot cards on players within the distance of the gun.