All the kids in Francisco’s class drew themselves. And then they got a class shirt with all the drawings. I think the idea is to wear it every Friday.
I got one for myself as well.
(Bemmy is the one farthest to the right, in the front row.)
43.614000-116.202000
Advertisements
Like this:
LikeLoading...
Related
This entry was posted on Friday, November 8th, 2013 at 3:30 pm and is filed under Life. You can follow any responses to this entry through the RSS 2.0 feed.
You can leave a response, or trackback from your own site.
Throughout the question, we only consider primes of the form $3k+1$. A reference for cubic reciprocity is Ireland & Rosen's A Classical Introduction to Modern Number Theory. How can I count the relative density of those $p$ (of the form $3k+1$) such that the equation $2=3x^3$ has no solutions modulo $p$? Really, even pointers on how to say anything […]
(1) Patrick Dehornoy gave a nice talk at the Séminaire Bourbaki explaining Hugh Woodin's approach. It omits many technical details, so you may want to look at it before looking again at the Notices papers. I think looking at those slides and then at the Notices articles gives a reasonable picture of what the approach is and what kind of problems remain […]
It is not possible to provide an explicit expression for a non-linear solution. The reason is that (it is a folklore result that) an additive $f:{\mathbb R}\to{\mathbb R}$ is linear iff it is measurable. (This result can be found in a variety of places, it is a standard exercise in measure theory books. As of this writing, there is a short proof here (Intern […]
I learned of this problem through Su Gao, who heard of it years ago while a post-doc at Caltech. David Gale introduced this game in the 70s, I believe. I am only aware of two references in print: Richard K. Guy. Unsolved problems in combinatorial games. In Games of No Chance, (R. J. Nowakowski ed.) MSRI Publications 29, Cambridge University Press, 1996, pp. […]
Let $C$ be the standard Cantor middle-third set. As a consequence of the Baire category theorem, there are numbers $r$ such that $C+r$ consists solely of irrational numbers, see here. What would be an explicit example of a number $r$ with this property? Short of an explicit example, are there any references addressing this question? A natural approach would […]
$L$ has such a nice canonical structure that one can use it to define a global well-ordering. That is, there is a formula $\phi(u,v)$ that (provably in $\mathsf{ZFC}$) well-orders all of $L$, so that its restriction to any specific set $A$ is a set well-ordering of $A$. The well-ordering $\varphi$ you are asking about can be obtained as the restriction to $\ […]
The two concepts are different. For example, $\omega$, the first infinite ordinal, is the standard example of an inductive set according to the first definition, but is not inductive in the second sense. In fact, no set can be inductive in both senses (any such putative set would contain all ordinals). In the context of set theory, the usual use of the term […]
I will show that for any positive integers $n,\ell,k$ there is an $M$ so large that for all positive integers $i$, if $i/M\le \ell$, then the difference $$ \left(\frac iM\right)^n-\left(\frac{i-1}M\right)^n $$ is less than $1/k$. Let's prove this first, and then argue that the result follows from it. Note that $$ (i+1)^n-i^n=\sum_{k=0}^{n-1}\binom nk i^ […]
I think it is cleaner to argue without induction. If $n$ is a positive integer and $n\ge 8$, then $7n$ is both less than $n^2$ and a multiple of $n$, so at most $n^2-n$ and therefore $7n+1$ is at most $n^2-n+1
