hyphenation - Hyphen: “well defined” vs. “well-defined”



Traditional English grammar teaches us that a well-defined function is a function that is well defined. With the hyphen in the adjective role before the noun and without the hyphen in the role of an adverb with a past participle after the noun. (E.g., see a question about well-organized, which is following the general rule, while the current one is about mathematical jargon.)


However, continuing an argument of Mr. West, a function that is well defined is a function for which we have done a good job of giving a definition, but a function that is well-defined is an object that has been given a valid definition as a function, with every domain element given a unique image. Said that, in the second meaning (an object that has been given a valid definition as a function, with every domain element given a unique image), should the mathematicians use the hyphen in "well?defined" in the after-the-noun position?


PS. I asked the same question at math.se, but they put it on hold, claiming that it could be off-topic there. Only one person gave his/her opinion, which I liked, but I'd like to hear other arguments, too.




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