# Binary operation

1. Oct 7, 2006

In the definition of a group on mathworld, http://mathworld.wolfram.com/Group.html, it is stated that the group operation is a binary operation, and it is stated that elements of a group must satisfy the four properties, including closure. Now, the definition of a binary operation, http://mathworld.wolfram.com/BinaryOperation.html, implies closure, so, isn't it unnecessary to talk about the property closure in the definition of a group?

Last edited: Oct 7, 2006
2. Oct 7, 2006

### AKG

What do you mean "isn't it sufficient to talk about the property of closure in the definition of a group?" It is not necessary to talk about the property of closure in the defintion of a group. But "not necessary" is not the same thing as "sufficient". Anyways, although it is not necessary, in theory, to talk about the property of closure, you are often just given a set S with a function * with domain SxS, and you have to verify that * is indeed an operation, that is, that closure does indeed hold.

3. Oct 7, 2006