Recent content by economist13

I know what I need to show to prove that T=t. i.e., O in T => O in t, since we are given t a subset of T. I just don't see how to do this with the information given. I guess I should have been more clear with what I need help with. I just am missing whatever key observation I need to make...

actually it is enough to know that if t is a subset of T and X is compact with T, then it is compact with t. Choose any open covering for (X, t), {Ui} for i in some index I, then it is also and open of (X,T), since t a subset of T. Since (X,T) compact, there is a finite open cover, {Ui}...

My bad, I forgot to mention that X is Hausdorff and compact.

Homework Statement Let X be a set and t & T be two topologies on X. Prove that if (X,t) is Hausdorff and (X, T) is Compact with t a subset of T, then t=T. (i.e., T is a subset of t).The Attempt at a Solution potentially useful theorem: (X,t) Hausdorff and X compact implies that each subset F...

A water distribution company in southern California gets its water supply from the north and sell it back to its customers in Orange county. Assume the following simplified scheme: 3 MG (millions of gallons) of water arrives from the north at the beginning of the month. The company can store up...

#12) Consider adding 0 in a creative way...so that you can factor out a 4 completely and have the sum of two numbers that are both divisible by 3.

A total of r keys are to be put one at a time, in k boxes, with each key independently being put in box i with probability pi , ∑pi = 1. Each time a key is put in a nonempty box, we say that a collision occurs. Find the expected number of collisions. My professor hinted that we should use...

yeah, it was really late when i pieced those ideas together, so I didn't think they were exactly right...I'll post the "solution" when they are posted if you're interested...

If you really think that is the case I suggest you look at modern economics again...in particular I might suggest Microeconomic Theory by Mas-Colell...or maybe Recursive Methods in Economic Dynamics by Stokey, Lucas, Prescott both standard PhD Micro/Macro books...

I think this is what I'm going to say... suppose to the contrary that e^x is not convex, i.e., suppose there exists a t in the closed interval 0 to 1 such that t * exp[x1] + (1-t) * exp[x2] < exp[tx1 +(1-t)x2]. also assume wlog that x2<x1 note that when t=0 and t=1, the two equations are...

hmmm, well, I'm an undergrad in a PhD microeconomics class...though only about half of the grad students have had analysis (I'm in the intro to analysis class now...) what you said makes sense...and I thought something along those lines, though didn't really know how to phrase it into a...

I know that if I can get 1 I can get 2, and vice-versa. The problem is I can't seem to get either...at least in terms of a mathematical proof. I can look at the graph and see that the set is convex...but that won't suffice on my HW.

Homework Statement prove the set is convex or give a counter example: 1. S = {(x,y) : y >/= e^x} 2. T = {(x,y) : y </= ln(x)} Homework Equations defn. of convexity (x1, y1) and (x2, y2) in S => (tx1 +(1-t)x2, ty1 + (1-t)y2) in S, 0 </= t </= 1 The Attempt at a Solution I think 2 will be...