Re: min / max and empty intervals - Entire and Missing Data
All
On 10 Jun 2011, at 11:02, Dominique Lohez wrote:
> A important point which must be noticed
>
> John is defining NaN
> as a LEVEL 1 CONCEPT
Let me clarify. At level 1, NaN is not a *value* that can be taken by a real variable, or can be returned by a real function. I'm following the standard mathematical formalism that for a real function f of n real variables, and x in R^n, f(x) either is "defined" and is a real number (if x in D_f) or is "undefined". An alternative scheme could be used, namely to say f(x) has some value NaN if x not in D_f, but that is a different formalism.
However it just pops out of the standard formalism, that NaN makes level 1 sense not as a *value* but as a particular *constant function*, namely the one with n=0 arguments and empty domain D_f.
John