1. The problem statement, all variables and given/known data Show that the set of all positive real numbers, with x+y and cx redefined to equal the usual xy and xc, is a vector space. What is the zero vector? 3. The attempt at a solution My attempt stops at me trying to decipher the problem. Are they asking me to take particular vector space rules and change them and show that, given the change in the rules, the set of all real positive numbers is a vector space? I'm also confused as to what they mean by xy and xc, in that x and y are both vectors and I'm not sure what kind of multiplication they want me to do.