7
votes
0answers
384 views
+50

How prove this polynomial inequality from a book

Question: Let $$f(X)=(X-x_{1})(X-x_{2})\cdots (X-x_{n})$$ be an irreducible polynomial over the field of rational numbers,with integer coefficients and real zeros. Prove that $$\prod_{1\le ...
9
votes
1answer
249 views
+50

Nonperiodic points of piecewise-linear homeomorphisms

Suppose $K$ is a compact polytope and $T$ is a piecewise-linear homeomorphism from $K$ to itself. Suppose also that $T$ is not of finite order (that is, for no $n \geq 1$ is it the case that ...
8
votes
3answers
518 views
+100

Does a left basis imply a right basis, without AC?

If $_DV_D$ is a $D$-$D$-bimodule, and we have a $D$-basis for $V_D$, do we still need AC to get a $D$-basis for $_DV$? (The original question appears below. But this shorter question gets at the ...
5
votes
0answers
434 views
+100

Zeta function double product

Is it possible to write the following double product in terms of the zeta function? \begin{align} &\prod_{i=1}^{\infty}\prod_{j=1}^{\infty} \frac{1}{1-(p_i\ p_j)^{-s}} \end{align} Extending the ...
6
votes
1answer
332 views
+50

What is the universal property of quotienting a normaliser of the subgroup?

Let $G$ be a group, $H$ a subgroup and $X$ a $G$-set. By taking orbits $X/H = X \times_H 1$ or fixed points $X^H = \mathrm{Hom}_H(1,X)$ we obtain a set on which $H$ acts trivially, and we've destroyed ...
4
votes
0answers
445 views
+50

Which universities teach true infinitesimal calculus?

My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by ...