Recent content by ecurbian

The states of the Schroedinger atom are indicated by several quantum numbers - principle, azimuthal, magnetic, and spin. From the point of view of differential equations, the first three can be derived by using radius and two angles and solving for seperable solutions. One then has what amounts...

Life Hi DCase Conway, Von Neumann, Nash, of course I am strongly familiar with -- I met Conway, just once, he talked about packing oranges into a box. But, this guy Mellies is new to me, I can read French, but the papers I downloaded were in English anyway and very interesting, so I'll have...

Loop, I realize you spoke to matt direct, and in my rushing out of the house this morning I did not properly read your posting, but, I still feel I have something to say here. The map f takes the set onto the sum of 2 to the powers of the m+1 elements of the set. This is the standard...

IMOH, arguments over terminology are politically dangerous, only attempt this if you are on good terms with your professor, or want to start a fight. In my experience, semi-group means associative binary operation, and monoid means associative binary operation with identity element...

Surreal This might be only an aside, but if we are talking about unification of mathematical disciplines using games theory, what about Conway's surreal numbers, and the extension to two player games? ps: thanks to Dcase for the ref to LaValle on the web.

Arithmetic approach This is one approach. Given a set of subsets of N with empty intersection, there can be at most one subset for each n in N, so there is at most a countable number of subsets. Given that the intersections are finite, there is at most a countable number of intersections...

If this is really true for EVERY A,B in D, then for all A in D, |A^A|<=m, that is |A|<=m. So D is not greater than Z^m (where ^ means power here) which is a countable set. Should that be, for every DISTINCT A,B in D? Sorry, just re-read the post, it was INFINITE subsets of naturals, so it...

"You do realize" that each expression when DIRECTLY implemented requires exactly the same number of gates (A.B)+(A'.B') requires two 'and's, two inverters, and one 'or', while (A+B').(A'+B) requires two 'or's, two inverters and one 'and'. At least if we are speaking of direct and-or-not gate...

There are several definitions of probability, some only work intuitively. Personally I use the axiomatic approach, and measure theory. But, I hope that the following gives an intuition for how to get from one to the other. If you are used to a probability being favorable/total outcomes, then...

In intuitive terms, the difference between two very large positive numbers can be small, even zero, thus indeterminate, but the sum of two very large positive numbers must be a very large positive number. Obviously (-inf)+(+inf) is also indeterminate. From the non-standard reals viewpoint...

There are many levels at which this problem could be taken, and to work out which more context would be required (eg, super-compressibility any one?), but in simple terms it looks like PV=NRT is the equation required. One way of putting it is that (PV)/(NT) is constant, knowing this you can work...

IMHO, putting it in a k-map shows visually THAT it cannot be minimized, and then only as a sum of products expression. It does not show "why". Also, if simplifying (x^2+2x+1) to (x+1)^2 is acceptable, then AB+A'B' = (A+B')(A'+B) is also simplifying in some sense. I think that "why" in this case...