Consider the following examples from which some definitions are derived:
Let us take an element from the set R of real numbers (say, the number 8) and another from the set L of lengths (say, 4m). Multiplication of both elements (8 x 4m) will render as result an element from the set L of lengths, namely, 32m. This constitutes an external binary operation of the first type with regard to the set of real numbers and the set of lengths. However, multiplication of two lengths (e.g. 4m x 6 m) no longer yields a length, but a surface (24m2). In such cases one speaks of an external operation of the second type with regard to the set of lengths.
I am translating the German terms äussere Verknüpfung der ersten Art (or der zweiten Art, depending).However, I have found he expression external binary operation somewhere. It did seem to refer to the second type. Could anyone confirm that? Would the first type be called unary operation?
I also found this comment: an external binary operation is a binary function from K × S to S. This differs from a binary operation in the strict sense in that K need not be S; its elements come from outside.
Does it hold for the other type? If not, where is the difference to so-called internal operation?
Thnaks in advance.