I have the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

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).

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Number of elements in a set

**Physics Forums | Science Articles, Homework Help, Discussion**