I have the following problem: Suppose I have a set called "the white chess pieces on a chess board". I could say the set contains the following: king, queen, rook, bishop, knight, pawn. This means the set contains 6 elements. I could also say the set contains: king, queen, 2 rooks, 2 bishops, 2 knights and 8 pawns. Hence, the set contains 16 elements. This is because I now see the 8 pawns, 2 bishops, 2 rooks and 2 knights as being different elements. You could say I gave them an additional property. So here is my question: Can we actually speak of "the number of elements in a set"? If I have a set of natural numbers between 2 and 5, I could include the number 4 more then once, by adding an additional property lets say colour. I could have a "red" number 4 and a "green" number 4. Now I realise that numbers are abstract and colour isn't, but I could also think of a more abstract property to differentiate between number 4's (like I did with the chess pieces).