Determine whether the following is a binary operation:
(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?