# hardmath

Knoxville, TN

uclue.com

Age: 63

Enjoys programming in Prolog.

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

When I cross the street, I look both ways: up and dn.

 51m comment a problem about truth in first order logicIs "structure" here the same as an interpretation of the (limited) language $L$ that is partly described? Is there a significance to the number of existential quantifiers $m$ as opposed to the number of universal quantifiers $n$ in prenex normal form $A$? 58m comment What is the significance of studying the steady state behaviors of a system? What information do steady state models provide us?@BenjaminLindqvist: Actually the property of "decaying to equilibrium" is a rather special property of some systems, one we are familiar with mainly because the systems that don't typically self-destruct. So it's survival of the fittest, in a sense. 1h reviewed Close If a subset of metric space $(X,d)$ like $S$ is closed and bounded, does it imply that $X$ is totally bounded? 1h comment If a subset of metric space $(X,d)$ like $S$ is closed and bounded, does it imply that $X$ is totally bounded?Obviously not. Are you really asking the Question that you meant to ask? If $S$ consists of a single point in $X$, regardless of what metric space $(X,d)$ actually is, then $S$ is closed and bounded. Why would this imply anything about $X$ being bounded? 1h reviewed Close Difference between $\mathbb C$ and $\mathbb R^2$ 1h reviewed Close Find the minimum polynomial of $u$ over $Q$ where $u=\sqrt3-(1+(5/2)^{1/3})^{1/4}$ 1h reviewed Reviewed What is the significance of studying the steady state behaviors of a system? What information do steady state models provide us? 1h comment What is the significance of studying the steady state behaviors of a system? What information do steady state models provide us?You seem to have tied the general question in the title to some kind of "exobiological" model, one I'm not familiar with. But generally the study of steady state solutions of dynamical systems is a good starting point for more realistic analysis. A steady state solution is "in equilibrium", so from a historical perspective one might compare this to static mechanics in engineering (vs. dynamic mechanics). While static or steady state analysis has some value in itself (e.g. when one wants to maintain equilibrium), it also has value as a preliminary to other studies. 2h reviewed Reviewed question on linear algebra word problems. 2h comment question on linear algebra word problems.Is something missing? After saying "...I tried this", there is only a problem statement (word problem). 3h reviewed No Action Needed Rouche theorem application 5h comment Maxima and minima of $f(x)=\binom{16-x}{2x-1}+\binom{20-3x}{4x-5}$.Okay, I'll put together an Answer based on the normal approximation I mentioned. 5h comment Depressed cubic rootsA quibble about notation. It's nice to couch an answer in terms of the discriminant $\Delta$, but you express it as a function of $c,d$ where the OP and linked Wikipedia page use $p,q$ as coefficients of a depressed monic cubic polynomial. I'd be happy to make an edit for you, but you are entitled to editorial control! 5h comment Maxima and minima of $f(x)=\binom{16-x}{2x-1}+\binom{20-3x}{4x-5}$.Yes, that looks good. I get $f(2)=728,f(3)=1617$. Do you wish to post an Answer, so future Readers will benefit from your reasoning? 9h revised Limit of the succession $\lim_{n \to{+}\infty}{n\sin(n\pi)}$minor punctuation, for clarity 9h reviewed Leave Open Limit of the succession $\lim_{n \to{+}\infty}{n\sin(n\pi)}$ 9h reviewed Close Finding the splitting field of $x^3-5$ over $Z_7$ 9h comment prove the unity cannot map to the zero in a ring homomorphism?You have a good idea about using the kernel (since it must be an ideal). The other important fact is that $f$ is supposed to be "onto". Since $K$ is a nontrivial ring, it contains something other than $0_K$. 9h reviewed Close Show that, $\lim_{N \to \infty}\prod_{k=1}^{N}\left(1+\frac{1}{2k}\right)^2-\prod_{k=1}^{N-1}\left(1+\frac{1}{2k}\right)^2=\frac{4}{\pi}$ 9h reviewed Leave Open Let $N = 3^{1000}\cdot 2^{2000009} +1.$ If $5^{\frac{N-1}{2}} = -1 \pmod N$, then $N$ is prime.