Two: my intuition says that exhaustively specifying the intended input output pairs would only hold marginal utility compared to testing a few well selected input output pairs. It's more like attaching the corners of a sheet to the wall than gluing the whole sheet to the wall. And glue is potentially harder to remove. The sheet is n-dimensional though.
Of course, for + it's relatively easy to intuit what it is supposed to mean. But if I develop a "joe's interpolation operator", you think you'll understand it well enough from 5-10 unit tests, and actually giving you the formula would add nothing? Again I find myself wondering if I'm missing some english knowledge...
Can you imagine understanding the Windows API from nothing but unit tests? I really cannot. No text to explain the concepts of process, memory protection, file system? There is absolutely no way I would get it.
That's the natural habitat for code, not formally specified, but partially functioning in situ. Often the best you can do is contribute a few more test cases towards a decent spec for existing code because there just isn't time to re-architect the thing.
If you are working with code in an environment where spending time improving the specification can be made a prerequisite of whatever insane thing the stakeholders want today... Hang on to that job. For the rest of us, it's a game of which-hack-is-least-bad.
Most of the tests I write daily is about moving and transforming data in ways that are individually rather trivial, but when features pile up, keeping track of all requirements is hard, so you want regression tests. But you also don't want a bunch of regression tests that are hard to change when you change requirements, which will happen. So you want a decent amount of simple tests for individually simple requirements that make up a complex whole.