Recent content by kimkibun

do you have a better explanation sir?

Homework Statement Show that x=cosx, for some xε(0,∏/2). Homework Equations The Attempt at a Solution Define f(x)=x-cosx, i want to show that for some aε(0,∏/2), limx→af(x)=0. is this correct?

sorry, you're right, i forgot the "disjoint" word. is there any other way (probably, easier) to prove that S is a disconnected set?

Homework Statement Let S={zεℂ: |z|<1 or |z-2|<1}. show that S is not connected.Homework Equations My prof use this definition of disconnected set. Disconnected set - A set S \subseteqℂ is disconnected if S is a union of two disjoint sets A and A' s.t. there exists open sets B and B' with A...

Good day! Im currently reading the book of Steven R. Lay's "Analysis with an Introduction to Proof, 3rd ed.". According to his book, if a subset S of ℝ contains all of its boundary then it is closed. But i find this wrong since if we consider S={xεQ;0≤x≤2}, then it can be shown that S...

but sir, according to the definition of path partition, it should be vertex-disjoint..

sorry if i posted this topic here..let P1 and P2 be a path partition of a graph.is it possible that P1 and P2 to have the same end vertices?

thank you so much sir! i really appreciate your efforts! God Bless you!

can you please show me how you get that? the mle for μ that i got is this, (Ʃxi/Ʃσi2)(Ʃ1/σi2) is it possible to find the mle of the parameter σi2?

Why is it that the set A={1/n:n is counting number} is not a closed set? We see that no matter how small our ε is, ε-neighborhood will always contain a point not in A (one reason is that Q* is dense in ℝ), thus, all the elements in A is boundary point, and we know that by definition, if...

i forgot to tell you that the n-observations was drawn out from a normal population..well anyway, is it possible that different variances might affect the maximum likelihood of the mean?

is it possible to estimate all parameters of an n-observation (X1,...Xn) with same mean, μ, but different variances (σ21,σ22,...,σ2n)? if we assume that σ2i are known for all i in {1,...n}, what is the mle of of μ?

here's the link sir http://www.sci.ccny.cuny.edu/~shpil/gworld/problems/probmat.html i agree with you sir when it comes to difficulty. my professor said that its a suicide for a graduating student to choose such topic. well anyway, thank you sir for your reply. btw, i enjoy reading the...

im having my undergrad math thesis right now, and the topic that i want to choose is the existence of torsion-free simple linear groups. (which i found here: http:///www.sci.ccny.cuny.edu/~shpil/gworld/problems/probmat.html) i just want to know if this topic is recommended for undergrad?

consider the set P={1/n:n is counting number}, my classmate said that P is equal to (0,1] but actually i don't agree with him since (0,1] contains irrational numbers. is he correct? also, is it possible for a set not to contain both interior and boundary points?