The noun form of "well-defined"

What’s the noun of well-defined (meaning that something is defined well in a mathematical sense). Also, could you show me more examples of the same structure/principle (of transforming the adjective form to noun)?

I guess it is well-definedness, but Google tells me that no one uses it.

Solution 1:

The noun is well-definedness, as you would expect.

I do not know what Google tells you, it gives me some 30k hits on this collocation. For example, in the Wikipedia article on well-defined:

... Or, in other words: A definition always claims its own well-definedness.

This particular case of conversion may be a bit counterintuitive because the well- should really modify an adjective rather than a noun. (Cf. well-order). On the other hand, it's only well that the noun refers unambiguously to its adjective; that's what a mathematician will appreciate.

Solution 2:

You could try precision, or exactness, both of which most dictionaries will recognise. Succinctness is a word, though it has a slightly different meaning, more well-expressed than well-defined.

It is worth remembering that in language there is often no precise, exact, or well-defined answer to a question like this. But there is often a succinct one.