/sci/ - Science & Math

Pic related is from some lecture notes which later go on to define an [math] \emph{internal} [/math] binary operation with the additional requirement that the unique element belong to V.

Is there any point in this distinction (there is none in the notes)? In other resources the "internal binary operation" definition is given under the name of a binary operation, and nothing is made of pic related.

Also, would I be wrong to call pic related an external binary operation? Wiki seems to suggest that's something quite different (K x V to V, not V x V to K)