Testwiki:Reference desk/Archives/Mathematics/2011 November 20

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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)

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)

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)

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)

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)

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)

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)

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

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)

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

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)