Why does "holiness" mean "set apart" (if it does)?

It is very commonly stated that "holiness" means "set apart". What is the scriptural, linguistic, or other basis for this repeated claim? Specifically: - On what basis is it claimed that the semantic domain of קודש (qodesh) and/or ἅγιος (hagios) includes the idea "set apart"? - On what basis is it claimed that this is the primary Biblical meaning? - Who first made these claims? Perhaps the following, from the entry in the *New International Dictionary of New Testament Theology* (Brown, ed) for **Holy** provides some justification for this question: > The basic idea [in the OT] is not that of separation (though that is favoured by some scholars, ...), but the positive thought of encounter [with divine power] which inevitably demands certain modes of response. An example of the sort of evidence that one might expect to find would be קודש occurring in synonymous parallelism with some other word with a clear meaning of "separateness". I would have expected someone to be able to quote some linguistic *evidence* for the "set apart" meaning of קודש and/or ἅγιος from a scholarly tome, but this hasn't happened so far. Indeed, several responses simply restate the purported definition (without any evidence), which seems to justify my statement that it is commonly stated as the meaning, and that it isn't entirely clear where this idea comes from. I'll keep digging.