ElijahJones

Show that if [MATH]n+1=(s+1)(m+1)[/MATH] then [MATH]\sum_{i=0}^{n}a^{i}=\sum_{i=0}^{s}a^{i(m+1)}\sum_{i=0}^{m}a^{i}[/MATH] for any natural number [MATH]a[/MATH].

Well when you put iot like that I think it fits the definition I mentioned below. The sigma field is a set of possible outcomes of sampling on W. Does W have a standard topolgy? Does s have a true field structure or is it just a name? At any rate if you now extend the set to include more possible samples you have added information its that simple. Or is s meant to include all possible samples already? The definition I gave below came form a good graduate level math text, I think it is correct.

And your into physics meta? Chemistry is more like it! Hellow all I am new. I have a BS in math with a physics minor, I am happy to help out anyone or to be theorize about anything. I am a graduate student in environmental science my focus is math modeling of environmental systems. Don't be afraid to send a PM for help with math problems. EJ

[MATH]sigma_0^{n}a^i[/MATH]

[MATH]sum[a^1,0..n][/MATH]

oh it does work, nifty. Let me tryot get the first challenge in latex. [MATH]sum(a^i,0..n)[/MATH]

Math tags? Something new to learn. [MATH] 2+2=1 mod 3[/MATH] That does not seem to work. Would you be willing to help me get started?

Cute! But really its not as daunting as it seems in fact #4 is really the hardest one of the bunch and the this refers to the answers to challenges 1-3 Mr. Clinton. It is not a debate about what the deifinition of "is" is.

What little I know of information theory is this. When a new piece of data is added to a set of data that we are using for a hypothesis test, the amount of information contained in that new piece of data is defined (by some) as the net change in certainty of our hypothesis. Thus if we get a smaller p-value we gained information against the hypothesis (p < .01 means reject the hypothesis). So in this way the information content of new data is not absolute it is related statistically to the relationship between the real world object of study and the existing data. This makes sense in real world applications because some information is not useful if it comes at the wrong time or is predicated by subtle differences in the underlying criteria. In real world information systems, new information is usually judged both by its quality with respect to the object of study and its quality with respect to current needs. There is a tendency in established information networks to insulate current knowledge against small amounts of information that imply major paradigm shifts. This can be both good and bad. I found the definition above in a rather old text (by non-mathematical standards) on information theory and would certainly like to learn more if anyone feels like talking.

(I missed a pair of parentheses) I thought to put this thread in the challenge area but it is math and all that stuff seems like philosophy. So here goes. I apologize for the pseudo-code but I do not have latex. Challenge 1: Prove that if n+1=(m+1)(s+1) then sum(a^k,k=0..n)=sum(a^[k*(m+1)],k=0..s)*sum(a^k,k=0..m) Challenge 2: Show that if n is odd then limit(a->infinity, ln[a](sum(a^k,k=0..n))-ln[a](sum(a^2k,k=0..[n-1]/2))) = 1 Challenge 3: Define an invertible function psi taking the set {limit(a->infinity,ln[a](sum(a^k,k=0..n))), limit(a->infinity,ln[a](sum(a^2k,k=0..[n-1]/2)))|n=1...infinity} to the natural numbers. Challenge 4: Explain what this means!

I thought to put this thread in the challenge area but it is math and all that stuff seems like philosophy. So here goes. I apologize for the pseudo-code but I do not have latex. Challenge 1: Prove that if n+1=(m+1)(s+1) then sum(a^k,k=0..n)=sum(a^[k*m+1],k=0..s)*sum(a^k,k=0..m) Challenge 2: Show that if n is odd then limit(a->infinity, ln[a](sum(a^k,k=0..n))-ln[a](sum(a^2k,k=0..[n-1]/2))) = 1 Challenge 3: Define an invertible function psi taking the set {limit(a->infinity,ln[a](sum(a^k,k=0..n))), limit(a->infinity,ln[a](sum(a^2k,k=0..[n-1]/2)))|n=1...infinity} to the natural numbers. Challenge 4: Explain what this means!