# VC-dimension of triangles in 2D space [closed]

I have been reading in multiple places (e.g. [1], section 4) that the VC-dimension of the class of triangles (in 2D space) is 7. The issue is that, for the case when 4 points lying on a straight line with alternating signs (like - + - +), I don't see why a triangle could separate the points. Where am I making mistake?

• You are getting the quantifiers in the definition of VC dimension wrong. The VC dimension being 7 means that there exists a set of 7 points that can be shattered and no set of 8 points can be shattered – Sasho Nikolov Mar 17 '15 at 0:47
• I am confused now. The thing is I can always find a set of 8 points such that a triangle shatters it. Draw a triangle, put 4 points inside it, and four points outside it. Right? – Daniel Mar 17 '15 at 1:09
• @Daniel: Shattering means that you have to be able to separate all +/- labellings of the same set of points, I think. – Huck Bennett Mar 17 '15 at 2:06
• A personal pet peeve, from teaching this stuff for years... A triangle (or any single concept) does NOT shatter a set of points. Only a CLASS of concepts can shatter a set. – Aryeh Mar 18 '15 at 9:38
• I don't think this is a research level question, and therefore it probably doesn't belong on this site. – Lev Reyzin Apr 18 '15 at 2:09