# hardmath

Knoxville, TN

uclue.com

Age: 61

Enjoys programming in Prolog.

Richard O'Keefe: "Prolog is an efficient programming language because it is a very stupid theorem prover."

 1h reviewed Approve suggested edit on prove that F is dense in C(X×Y,R) ? any help! 19h comment Find the roots of the following polynomial equation..As you know a cubic polynomial over the complex numbers has three roots, counted according to multiplicity. If you can find a real root (a version of Rational Roots Them. applies here), then you can remove a corresponding factor to get a quadratic polynomial. Then things should be simple. 22h comment $\ f \colon X \to X$ ,continuous function where X is compact,Hausdorff space.Show $\exists A$ st $f(A) =A$.@Seirios: Of course trivially $f(\emptyset) = \emptyset$, but I suspect the goal is to prove the statement for nonempty $A$. Here's an example to show that without topology, the trivial solution is the best one can do. Consider $f(x) = x+1$ on $\mathbb{N}$. Suppose $A$ were a nonempty set s.t. $f(A)=A$ and let $x$ be the least element of $A$. Since $x \in f(A)$, there must be $y \in A$ s.t. $x= y+1$, contradicting minimality of $x$. 23h comment Boole's functions' domain is D = {1, 2, 3, 4}. Find ∃xF(x, 2), when F(x, y) = 1100 1111 0011 0101.I suspect the expressions for $F(x,y)$ are two-dimensional and intended as lookup tables for rows designated by $y$ and entries within a row (columns) designated by $x$. This sort of Question is not a good fit for Math.SE since the content is really the poster's confusion about what their homework means. Far better to ask the teacher about it. No one else will ever benefit from learning how the poster got squared away, and the poster is unable to assist in clearing up the confusion because of language and typographical barriers. 23h awarded Yearling 1d revised Algorithm to find all feasible partition of a setWorked out the algorithm details for the example problem, only one solution 1d comment Contraction of compact setsPersonally I find the thread of your argument hard to follow, and I suspect it could benefit from some preliminary guidance to the Reader how you plan to proceed. You are arguing by contradiction assuming no $A$ s.t. $f(A)=A$ exists. It's hard to tell if the use of $A$ in the next to last paragraph ($A=U_1$) adds anything to the argument. Presumably you reach a contradiction just working with $U_1$. 1d comment $\ f \colon X \to X$ ,continuous function where X is compact,Hausdorff space.Show $\exists A$ st $f(A) =A$.Often the "proof to be checked" is included in the body of the Question for these types of questions. I'll vote to reopen, but keep it mind for future requests. 1d comment If $x_1^3+x_2^3+\ldots+x_t^3=2002^{2002}$, find minimum value of $t$ such that the predefined condition is satisfied for all natural numbers $x_i$'s@user133281: Good comment, but don't change the meaning of the Question to "help" the OP. They are actively engaged and will likely respond to your point. 1d revised If $x_1^3+x_2^3+\ldots+x_t^3=2002^{2002}$, find minimum value of $t$ such that the predefined condition is satisfied for all natural numbers $x_i$'sEdited title to agree with change in body 1d awarded Supporter 1d awarded Autobiographer 1d answered Algorithm to find all feasible partition of a set 1d comment Algorithm to find all feasible partition of a setOf course we can eliminate any sets in $S$ that are empty or that are not subsets of the target, $T=\{1,2,3\}$ in your example. If $S$ were all of the nonempty subsets of $T$, the number of solutions you want to find is called Bell's number $B_n$ where $n=|T|$. Since generally there are so many of these to construct, I would guess that a backtracking algorithm (taking candidate subsets from $S$ in some predefined order) would perform adequately. 2d comment Linear Algebra Api for c++ using external memoryThis seems more appropriate for the Computational Science or the Software Recommendations site as it lacks much of a career programming angle. 2d comment Why is this the method to getting transpositions from disjoint cycles?@Frumpy: You seem to be applying the permutation more than once. If you apply it once, then it maps 2 to 4. Of course the permutation maps 4 somewhere also (it maps all the items 1 through 7 to some value, rearranging them so we call it "permutation"). But if you apply the mapping once, the disjoint cycle representation tells us quite clearly where 2 goes (check your original Question). 2d comment Siamese twins provingDepending on the level of course taken, a word about why 1 is not considered a prime could be helpful. 2d comment Siamese twins provingOkay, I'm convinced that (for positive integers) the only pair of primes that differ by one are 2 and 3. Apr 15 comment Limited completeness and restricted quantifiers+1 for using the phrase "model automorphisms". Apr 15 comment Limited completeness and restricted quantifiersOops, I meant to say "does not suffice" in the last Comment. Perhaps the distinction regular and strongly regular graphs is analogous, or more to the point, vertex transitive but not edge transitive.