Recent content by seeker101

Any suggestions on how to simplify the log (m+1) terms that arise when proving the following statement using induction for m >= 1? (log to the base 2) [PLAIN]http://dl.dropbox.com/u/471735/recurrence%202.png

I managed to solve it. Thanks anyway! For those interested: It's quite straightforward using double induction.

[PLAIN]http://dl.dropbox.com/u/471735/Recurrence.png

Any suggestions on how to approach solving: \Psi(m,n) \leq \Psi\left(\left \lfloor\frac{m}{2}\right\rfloor,n_1\right) + \Psi\left(\left \lceil\frac{m}{2}\right\rceil,n_2\right) + 16n^*+11m \lceil\text{log }m\rceil where n = n_1 + n_2 + n^*

Many thanks!

Any suggestions on how to prove that \prod^{\infty}_{j = 1} \left(1-\frac{1}{2^j}\right) is greater than zero?

Much appreciated! Thank you.

Does anyone have any suggestions on how to go about proving that \left\lceil\frac{1}{2}{\lceil \log m\rceil}^2\right\rceil is less than m-1, for m > 64? (using log to the base 2)

Sorry. I left something out. Suppose now the definition of a http://en.wikipedia.org/wiki/Simple_function#Definition" also requires the events A_k to be mutually exclusive. How can we now show that the sum of two simple functions will also be simple?

I can intuitively see why the sum of two http://en.wikipedia.org/wiki/Simple_function#Definition" is also simple. But can someone point me to a formal proof?

Basic question: meaning of "partition of R into maximal connected intervals" What does the phrase "partition of R into maximal connected intervals" mean? The full sentence: "Let I_1, I_2, ... ,I_m be the partition of R into maximal connected intervals with disjoint interiors."

Could someone point me to a book that has a proof of the above statement? Thanks in advance!

A basic qn:An infinite sum of vectors will also be a vector in the same vector space? By definition, the sum of any two vectors of a vector space will be a vector in the same vector space. But does this mean the sum of an uncountable or countable number of vectors will also be a vector in the...

I was trying to prove that the sigma algebra generated by the set of open intervals is the same as the sigma algebra generated by the set of open sets. This proof devolves into proving the statement in the title. I think rational numbers must be brought into the picture to prove this stmt but I...

A basic question: What does "closed form" mean? "The point here is that \sigma algebras are difficult but \pi systems are easy: one can often write down in closed form the general element of a \pi system while the general element event of \mathbf B \mathbf is impossibly complicated" - From the...