Recent content by jeremy22511

@PeroK @Gaussian97 Thanks! That's about the explanation I wanted.

My probability class has me wondering about pure math questions now. We started with the axioms and are slowly building up the theory. Everything was fine but then a definition of Conditional Probability P[A|B] = \frac{P[AB]}{P} appeared and it's just not sitting right with me. I know that...

Thanks! What about the case with positive random variables? I probably should have given some context with my question. I was trying to make sense of using the two-tailed region in hypothesis testing by showing that it minimizes the expected value of P(H0 | z-score in critical region). But this...

If E(X1)>E(X2), does it mean that E(1/X1)<E(1/X2)? Thanks!

If there is a bijection between R and R2, then why can't a point on a plane be represented by one real number instead of two?

@HallsofIvy I still remember you answering some of my questions a few years back. Thank you again :) That's not what I mean though, and frankly I'm still a bit confused. Riemann's non-Euclidean geometry can be used to study a sphere surface, and get properties of that sphere surface, but...

Thank you for your answer, but that doesn't answer my question. Creativity is a crudely defined word that does not fit in any model of math or science. It's like saying 'it's luck' when all it is is probability.

So I was wondering why a single problem can have two entirely different approaches (based on contradictory axioms) to solving it? For example, consider sunlight. Sunlight always comes from a slightly different direction than we see because of refraction. They can be studied with Euclidean...

Thanks. That really helped. Jeremy

Can somebody prove the equivalence statement of two real polynomials in one variable x for me? My Math teacher just told us to remember it as a definition and so I didn't get any proof for it; I attempted to prove it myself and ended up confusing myself with a lot of symbols. So, can somebody...

I suppose I should post it here. It's not really a homework problem... And my question is: Is the validity of the vector approach in mechanics entirely based on its consistency with experimental results? Every time I do a question, I use the usual component resolution technique unique to...

Thanks very much XD I just needed a confirmation.

Very basic (I'm a high school student): Background I'm studying a chapter in my textbook titled 'Energetics'. It touches on enthalpy changes. It mentions that bond-breaking processes are associated with energy absorption and bond-forming processes are assciated with energy emission...

Diatomic molecules... Forgot that >.< Thanks for the thread. (Colors of chemicals are really frustrating!)

Please help!