not its complementary (“numbers divisible by perfect squares”). See

http://en.wikipedia.org/wiki/Square-free_integer for an heuristic

proof. ]]>

Our students are taking measure theory in parallel to this course, plus optimisation and functional analysis courses, so this is the “easy” one in the series. Plus, they had several weeks to practice on the exercise booklet, knowing the exam would come from those. Obviously, some did not practice….

]]>thanks, this sounds too clever by half for our beginners, however I have not received their code file from the computing department so who knows?!

]]>I hope so too!!!

]]>Thanks, this was a typo, we should have had a>0 from the start!

]]>foo<-as.character(1:9999)

foo<- gsub('[2,4,5,6,7,8,9,0]','',foo) only 1s and 3s left

foo<-as.numeric(foo)

#find positive diffs in foo ]]>

F(x) = 1 if x >= a

F(x) = (x/a)^k if x < a

Furthermore, you can't take a in R, as a = 0 is not well defined (Though I suppose you could make it a point mass at 0.)

]]>