Comment by ccppurcell

I was just referring to one of the early sentences saying breakfast is a vector space. If you allow arbitrarily many (say) eggs so that two eggs and one egg are different breakfasts, you get a cone inside R^d. If you normalise and consider the ingredients as fractions of a whole (so that 1 egg and 2 eggs are both represented by the 1.0 egg breakfast) you get this simplex structure and the coordinate system you mentioned. But that's still not a vector space as there are not inverses in general. At best it can be embedded in R^d.