Mathematics desk
< November 19	<< Oct \| November \| Dec >>	November 21 >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

November 20

Extended Schur's theorem

Hello all,

I'm trying to deduce from Ramsey's theorem that whenever $\mathbb {N}$ is finitely coloured there exist x, y, z with $\{x,\,y,\,z,\,x+y,\,y+z,\,x+y+z\}$ monochromatic.

I've seen a proof of Schur's theorem (effectively finding x, y, x+y with $\{x,\,y,\,x+y\}$ mono) using Ramsey's theorem before, and this seems like a similar but adapted version. Could you prove the above (which seems to be a strengthened Schur) using Ramsey's theorem too? I've tried but haven't gotten anywhere, could anyone please give me a hint? Thank you! Frimgandango (talk) 13:55, 20 November 2011 (UTC)[reply]

It's certain true; it's called Folkman's theorem. I don't know how the proof goes, though.--121.74.125.249 (talk) 20:57, 20 November 2011 (UTC)[reply]

Yes, I've seen Folkman's theorem before. However, I've been told to "deduce it from Ramsey's theorem", presumably rather than using Folkman's theorem which I also covered in my lectures later on; it becomes trivial very quickly using Folkman's theorem of course. Frimgandango (talk) 21:04, 20 November 2011 (UTC)[reply]

Addition Problems

What is one add one? I.e. 1+1? This is not a homework question. Thankyou for your time. 94.195.251.61 (talk) 16:30, 20 November 2011 (UTC)[reply]

There are 10 kinds of people in the world: those who understand binary and those who don't. Dbfirs 17:08, 20 November 2011 (UTC)[reply]

Usually 2, of course. It depends on your definitions of 1 and +. You might be interested in the classic book Principia Mathematica, or the articles on modular arithmetic, group theory, or the binary numeral system. Bobmath (talk) 18:02, 20 November 2011 (UTC)[reply]

I've said it before, and I'll say it again - it's -1 in

\mathbb {Z} _{3}

, 0 in

\mathbb {Z} _{2}

, 1 in boolean algebra, 2 in

\mathbb {Z}

, 10 in binary and 11 in Gray code. -- Meni Rosenfeld (talk) 18:42, 20 November 2011 (UTC)[reply]

1+1 is a sum. Hope that helps, Qwfp (talk) 19:20, 20 November 2011 (UTC)[reply]

This question has been asked on the reference desk before. Please search the archives before asking a new question. Widener (talk) 02:08, 21 November 2011 (UTC)[reply]

For a few other answers, see 1+1 (disambiguation). – b_jonas 13:27, 23 November 2011 (UTC)[reply]

Schaum's Topology

There is a new edition of Schaum's General Topology by Seymour Lipschutz, but when I look at it on Amazon, it seems to give me only the old version. Has anyone had any experience with the new version, and is it better? I only do this stuff in my spare time as a hobby (and I don't get much time for it) so I'm looking for something that avoids excessive theory. I also have the Schaum's set theory guide, so I don't need more stuff on cardinality. I'm interested in stuff like connectedness and compactness etc., if that helps. Thanks, IBE (talk) 20:05, 20 November 2011 (UTC)[reply]