This is an question from the book "A concise introduction to Pure Mathematics". I understand that it looks like a homework question but it's the first chapter and there are no answers for even questions. As I am independently trying to make my way through a bit of maths I was hoping I could get some help.
The real reason I am stumped is I don't yet have a firm grasp on what a proof is (at which point its conclusively proven).
I think the negation of the statement would be
"There exists a real number less than every positive real number that is positive"
I am tempted to use square root and say
n > 0
n = sqrt(k)
therefore k > 0
I don't think I have proven anything.
Also: Could someone please advise and perhaps throw some beginner texts my way?