Would one of the mathematically-inclined people mind taking a look at bitbucket.org/rivanvx/beamer/issue/96/… and suggesting what I should change :-)

@AlanMunn, @egreg: I have to confess:

"Brute force - if it doesn't work, you're just not using enough."

@JosephWright Change where?

@AndreyVihrov In the proof to make it correct!

I wrote down the proof as I knew it since school: mathbin.net/67375  But I still can't see the mistake (2·3·5·…·13+1 is not prime). Would this be a suitable quiestion for math.tex.sx?

Oh, I somewhat see it now…

Simple questions can sometimes be turned into simple packages

Just committed two new packages that do very simple stuff

in the spirit of "Do one thing and do it well"

Nice! Which ones?

Correct proof: mathbin.net/67395

@PauloCereda github.com/raphink/impnattypo and github.com/raphink/nowidow

I don't fully like how it sounds, so please make better suggestions.

@AndreyVihrov Great: That will help close another bug :-)

@AndreyVihrov Every (finite) set of primes cannot contain all primes. Proof. We know that every number bigger than 1 is divisible by a prime; let n be the product of the numbers in the set; if the set is empty, then clearly it doesn't contain all primes, so we can assume that n>1; then n+1 > 1 and so it's divisible by a prime which cannot be in the set. QED

Note that (1) this is not a proof by contradiction, because it constructs a prime not in the set, namely the minimal divisor (bigger than 1) of n+1; (2) it's not claimed that n+1 is prime.

@Werner w.r.t. the hyphenation question: My original comment was about your pre-edit version of the answer. (I can delete the comment.) But I guess the focus of the problem isn't really lack of hyphenation points for the word (which TeX does seem to know) but with the fact that the word is a compound containing a hyphen.

Whilst I agree that it isn't phrased well, then I don't see a problem with the proof as it stands in the current beamer manual. It starts with Suppose p were the largest prime number.. Then it constructs a number which is not divisible by any of the prime numbers up to p. In the universe in which p is the largest prime number then this number must be prime. Reason: it is not divisible by any prime smaller than it, since p was the largest prime, (ctd)

(ctd) and a composite number is always divisible by a prime smaller than it.

This is the problem with "proof by contradiction". We set up a universe that (we shall show) cannot exist. We then show that it cannot exist by finding some proposition that is both true and false that holds within it. But while we are in that between stage, we work within the imagined universe and have to pretend that it is real. So if we assume that p is the largest prime number, we have to play by those rules. In that universe, p! + 1 is prime and that is the desired

contradiction.

But far better to have a positive proof, such as that by egreg above. To have it in a list, maybe the following would work:

@AndrewStacey: pardon my ignorance, but I'm curious: what does k | q mean?

@PauloCereda Just k divides q.

@AndreyVihrov Wow, thanks. I feel like an idiot. I'm used to see | like in the set description you wrote (I use / for division).

@AndrewStacey, @egreg. Remember that what I need is Euclid's proof, not just any proof, otherwise the fun is spoiled :-)

@AndreyVihrov The proof I presented doesn't actually require such definitions; but it uses a fact proved previously that all numbers greater than 1 are divisible by a prime number and also (which actually is a key point) that n+1 is not invertible.

@PauloCereda Note that / is an operator, but | denotes a relation. "k | q" is either true or false. This notation is uneasy for me, too, because I'm used to the "q <three vertical dots> k" notation that is widespread in Eastern Europe.

@AndreyVihrov aaah thanks! I got it now. ;-)

@JosephWright So the proof I presented is what you need: also Euclid constructed a new prime from any given multitude of primes.

@egreg I thought his was by contradiction (in general terms)?

As Euclid wrote his work well before modern proof methods, I realise it's not quite the same as you'd do today :-)

@egreg I think you use the definition of a prime number through the fundamental theorem of arithmetic.

@AndreyVihrov The usual definition is: p is prime if it's > 1 and from a | p it follows that a=1 or a=p.

friends, which tool should I try for converting my tex files to html? Probably TeX4ht?

@PauloCereda Yes, definitely. It works pretty well as long as you don't have lots of uncommon packages.

and as long as you stick to pdftex

You should also check out tex.blogoverflow.com/2011/07/getting-latex-on-to-the-web

thanks, I'll take a look. Let's hope for the best. =)

@PauloCereda: @AndrewStacey also has a new package to generate web contents from TeX

Haven't tried it yet, but that's what he uses to publish on the TeX.SX blog.

@Raphink: Cool! I'd like to try it too.

He mentioned it on here a few days back. You might find it in the history.

@Raphink Yes. Karl Berry has the following in the tex4ht bug tracker: "We need to write fontspec.4ht for use with xelatex. This is a big job! " So they are aware of it. We should understand that tex4ht was the creation of one person (Eitan Gurari) who died very unexpectedly in 2009 and so it will take a while before re-development is up to speed.

yes

@AndrewStacey's internet.cls makes use of fontspec as far as I understood.

Found the link!

I need to try xelatex or even lualatex.

Oh you certainly do

see my post on the subject on the blog (and the comments, they're interesting, too).

tex.blogoverflow.com/2011/08/a-short-journey-with-latex

@PauloCereda if you want to discover fontspec, you can try building babyloniannum.

It makes a big use of fontspec and shows the kind of things you can do with it.

Also, github.com/raphink/geneve_1564 shows the kind of advanced OTF features you can use.

@Raphink Thanks, I'll certainly try. =)

the code is rather simple and you'll probably spot the fontspec specific parts easily.

@PauloCereda They're really not that mysterious. See tex.stackexchange.com/questions/21736/… Many things that work with XeLaTeX also work with LuaLaTeX. On the differences: tex.stackexchange.com/q/36/2693 and tex.stackexchange.com/q/23598/2693 Of course, LuaLaTeX has the full power of Lua as well, which makes it interesting for all sorts of other reasons. See tex.stackexchange.com/q/70/2693.

(Maybe all these questions are linked in Raphink's blog post too.)

@AlanMunn I should probably have linked the questions in my blog post, indeed, but I don't think I did.

@AlanMunn Great resources, thanks. I'll read them.

Alright, off to bed

laters

see ya!