... 2.7027027.... being very close to e. ... 2^11*3^26=5205741216417792 2^8*3^28 =5856458868470016 2^5*3^30 =6588516227028768 2^2*3^32 =7412080755407364 Each...
... More importantly 2x2=4 ... not very close to e. The addends must be 2 or 3, not because they are closer to e, but because an alternative to the addend 5,...
Heuristic formulation: You're playing a game in which you get to flip a coin over and over as many times as you want. When you choose to stop, you receive as a...
I don't think my last reply posted, so I'll retype it. I'm conjecturing that if you flip long enough, you're eventually going to get a ratio of at least 1/2,...
Hold the horses. Even my below strategy isn't optimal. Under my idea, I've just said to stop if you flip TH, and collect .50. But how about instead, we...
... No. You can flip forever and still get only 0s. What you want to say is that, for any fixed e > 0, the probability P_(e,n) that the ratio for the n first...
... But ... ratio ... Yes, but you have to keep in mind that if you keep flipping forever, you don't win anything. So, at one point or another, you may have to...
I never meant to flip forever. What I meant is that if you flip long enough, I'd suspect that sometime before infinity, you're going to eventually make up the...
... I suppose that depends on what you mean by "can," since that event has probability 0. ... ratio ... If I'm reading this right, it just says that the ratio...
... That's a good way of describing what I was thinking. Assuming that the probability of 1/2 never being reached is zero, then my expectation argument still...
Your argument (that .75 is a lower bound for the payoff which can be reached) is very convincing and I agree with your intuition that waiting for a .5 ratio...
Hi Let f belongs to BV[a,b] and f is continuous at t such that a<t<b; How to prove that total variation of f on [t,t+1/n]-->0 as n-->0. Send instant messages...
Hello ... Let e be a fixed positive real (e>0). f being continuous at point t, there exists a positive integer N_e such that for any x in [t,t+1/N_e],...
... Formally easy, but an example in a well-known group (a group of matrices for instance, or a non-commutative field like the quaternions) may be trickier to...
Back to a formal proof. Assertion: no optimal strategy exists (according to the meaning given in the rigorous description of the problem). Proof: Assume such a...
... where ... that ... the ... 1/2. ... probability ... expectation ... In case 2 for example, if T* is modified it would cause the payout for the particular...
... where ... The natural probability space for this problem is {0,1}^N, where N is the natural numbers. As video_ranger pointed out, the properties of T*(w),...
... http://uk.messenger.yahoo.com Since f is BV, f=g-h, where g and h are nondecreasing. Let G(s)=g(s) for s<>t and G(t)=lim_{s-->t,s>t} g(s), which exists...
x belongs to real numbers, every function accord with f(x-4)+f(x+4)=f (x) is periodic function, so what's the minimum common period of all these functions...
Hello ... =f ... all ... f(x)+f(x+8)=f(x+4), and, replacing in the first equation gives: f(x-4)+f(x+8)=0, f(x)+f(x+12)=0, f(x+12)=-f(x) (=> f(x+24)=f(x)). This...
... Thanks for ur solution of the problem but the solution u have provided seems to be a example of the validity of the theorem. There are other examples for...
Try to answer this proble (Its rather well known but i wish there must be someone who doesnt know it.) How many squares are there on a chess board (There are ...
... Perhaps a newer challenge/variation would be to find how many rectangles [none of them squares] there are. If we consider other possible connections of the...
... An equivalent formulation of the original question is "prove there exists a group G and two elements a and b of finite order such that ab does not have...
... The expression on the right, regarded as a function on the (x,y) plane with the origin removed, is constant along lines through the origin, so you may as...
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