Recent content by VonWeber

Rings in measure theory, as in rings and algebras. I have that in the title of my post but forgot the word 'theory'... These rings are defined to be classes of sets closed under unions, closed under set differences (aka relative complement), and containing the empty set. I think I've made a...

Homework Statement Let D be a class of sets of space X. There exists a unique smallest ring, R, containing D The Attempt at a Solution I'm working on the existence part. If D were finite, I think that it would be possible to use set differences to find a set, D', of smaller sets...

My analysis text mentions in passing that the real numbers can be constructed rigorously starting from set theory. I was wondering if there were a resource on the web that might go over this and show the proofs of how this is done?

Thanks, perfect. Sometimes just hearing something said with different wording helps people get unstuck.

Homework Statement I'm reading a book on analysis independently. There is a Theorem that R is complete, i.e. any Cauchy sequence of real numbers converges to a real number. He let's a1, a2, a3, ... be a Cauchy sequence, then considers the the set: S = { x an element of R : x ≤ an for...

I've always been suspicious of the yogurt fad. The bacteria would have to survive until it reached the colon assuming the acidiphilous that thrive in milk are suited to live in the intestines.

I live in housing for students where we share a kitchen and prepared meals nightly. I'll watch people cooking the meals for everybody handle food with their bare hands and pick up shared food in the fridge like blocks of cheese with their bare hands. And when suggest that they not do so, they'll...

Is it a myth that the bodies resistance to germs be "built up" by exposure? I'm not sure is this is more a medical question, but I'm thinking it's more of something biologists would address? When I see people criticized about eating things that have come into contact with unclean or doing...

There isn't a course at my university for Bayesian stats, but I was wondering if it would be possible to teach myself. Does anyone know of any good intro texts or online resources for leaning Bayesian Statistics? Also I want to learn to use R some over the break. Does anyone know of any good...

So I take for one part: y² = (mx)² + 2mx√(a²m² + b²) + a²m² + b² substituting for y² in the equations for an ellipse I get: x²(1/a² + m/b²) + x[2m√(a²m² + b²)/b²] + a²m² = 0 I don't see how to make it clear that this has a repeated root, and I'm unclear on why that means it is a tangent to the...

Yeah, of course I meant tangent. don't be so nitpicky

Homework Statement I was tutoring a student and could not answer one of his questions. Prove that y = mx +- square root( a^2*m^2 + b^2 ) is the equation for two lines passing through an ellipse Homework Equations (x/a)^2 + (y/b)^2 = 1 is the equation of an ellipse The Attempt at a...

Homework Statement Are all disjoint events also mutually exclusive? And if events are independent does this also mean that they cannot be disjoint? Homework Equations no relevant equations The Attempt at a Solution In probability disjoint events are events that have no...

I want to start over. Are any uncaused causes known to physics? That is are there anything that causes changes, motions, etc. that we can observe that we have no reason to think was itself caused by anything itself?

Well I think girls tend to become wary of all men. They may not think he is a rapist or stalker for sure, but they will look for signs or anything that doesn't quite seem right. It's often better to be on your guard even if it means not giving someone the benefit of the doubt.