Originally Posted by

**ulysses123** Determine whether the following is a binary operation:

S={1,-2,3,2,-4} a*b=|b|

(where a*b is the "generic" notation for any binary operation)

Now to my understanding a binary operation takes two elements from a set, and creates a third from the same set via a binary operation. Now |b|

requires the first element to be b and the second elemet to also be b.

But the magnitude is b times b and then taking the square root, so is this classified as more than 1 binary operation.

Also for the difinition of a binary operation does the third element have to be unique? or is this only for a one to one map?