This is an excellent documentary about a horrible ongoing tragedy. But there is a lot of hope in the story; John Bul Dau, one of the “lost boys of Sudan” the movie is about, is inspirational, a great leader. In the midst of all their suffering, I could not believe how much energy and optimism he displayed. He is truly an admirable person.

Part of the documentary follows several kids that are relocated to the States (thanks to Catholic Charities International). I found particularly interesting to see the culture clash that the group suffers, arriving to and having to survive in the States with what looks like very little assistance.

Although they are very grateful, we learn that the older ones have to hold one or two jobs in order to pay back the cost of their move. Of course, the jobs they find are not particularly appealing or well paid, plus they have to face discrimination and ignorance. The younger ones, on the other hand, get to go to school and several of them try very quickly to absorb the American life style, leaving behind their roots and traditions, which leads to an interesting clash with people like John Bul Dau, who makes every effort to keep their memory and connections alive.

I highly recommend this moving and sobering documentary.

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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 […]

Suppose $M$ is an inner model (of $\mathsf{ZF}$) with the same reals as $V$, and let $A\subseteq \mathbb R$ be a set of reals in $M$. Suppose further that $A$ is determined in $M$. Under these assumptions, $A$ is also determined in $V$. The point is that since winning strategies are coded by reals, and any possible run of the game for $A$ is coded by a real, […]

Yes. This is obvious if there are no such cardinals. (I assume that the natural numbers of the universe of sets are the true natural numbers. Otherwise, the answer is no, and there is not much else to do.) Assume now that there are such cardinals, and that "large cardinal axiom" is something reasonable (so, provably in $\mathsf{ZFC}$, the relevant […]

Please send an email to mathrev@ams.org, explaining the issue. (This is our all-purpose email address; any mistakes you discover, not just regarding references, you can let us know there.) Give us some time, I promise we'll get to it. However, if it seems as if the request somehow fell through the cracks, you can always contact one of your friendly edit […]

Consider any club subset of $\kappa $. Check that it has order type $\kappa>\lambda $, and that its $\lambda $th element (in its increasing enumeration) has cofinality $\lambda $.

A very nice introduction to this area is MR0891258(88g:03084). Simpson, Stephen G. Unprovable theorems and fast-growing functions. In Logic and combinatorics (Arcata, Calif., 1985), 359–394, Contemp. Math., 65, Amer. Math. Soc., Providence, RI, 1987. Simpson describes the paper as inspired by the question of whether there could be "a comprehensive, self […]

There are continuum many (i.e., $|\mathbb R|$) such functions. First of all, there are only $|\mathbb R|$ many continuous functions, so this is an upper bound. On the other hand, for any real $r$, $f(x)=x+r$ satisfies the requrements, so there are at least $|\mathbb R|$ many such functions.

I'm posting an answer based on Asaf's comments. The following reference addresses this question to some extent: MR0525577 (80g:01021). Dauben, Joseph Warren. Georg Cantor. His mathematics and philosophy of the infinite. Harvard University Press, Cambridge, Mass.-London, 1979. xii+404 pp. ISBN: 0-674-34871-0. Reprinted: Princeton University Press, P […]