There are many applications of "pairwise", for instance different, disjunct, orthogonal, independent, intersecting, connected, and many more. Some of them like "pairwise intersecting" or "pairwise connected" seem meaningful. But most of them appear to express no more information than with "pairwise" deleted. Who introduced this expression in mathematics in what framework?



Who invented the expression "pairwise different" and what is its advantage over "different"
After some pondering about my question (and after finding out that this expression turns up in one of my books) I would like to revise my position a bit: "Pairwise orthogonal" seems redundant, but that may depend on the implicit understanding of quantifiers that have to be added to colloquial speech. "A set of orthogonal vectors" could in principle mean that for every vector there is an orthogonal one. Of course this is not the meaning attached to the word in general in mathematics. But can it be excluded a priori?


Nevertheless my question remains open (until it will be closed): Who invented the word "pairwise" or "paarweise"? I do not believe that Hilbert 1903 was the first, but do not know either and am curious to know it.


