On commonly-used magic systems (5/?)

I'll have to retract my earlier statement: the element N of non-elemental spells is the unique element such that for all elements E and all targets t∈T, D(E,t) = D(E,t) * D(N,t) — or, equivalently, for which every element is a hybrid element of itself and N. This is less restrictive than the former statement (t∈T, D(N,t) = 1); it is equivalent thereto iff * is associative and invertible on some extension of R. (Which is exceedingly rare, as R will usually include 0 to indicate that an enemy is immune to an element.) This allows enemies to be immune to (via, e.g., antimagic field) or reflective of (via, e.g., Reflect) all magic.

Surprisingly, by this definition, status-inflicting spells are rarely non-elemental: while in some cases (such as Skies of Arcadia) the status magics are explicitly folded into the obvious elemental system, more often certain classes of enemies will simply be exempted from them. (When was the last time you saw a boss that was vulnerable to an instant-death attack? — okay, other than Revive Kills Zombie. And no, the Vanish/Doom trick doesn't count: Vanish changes the value of t the same way Reflect does.)

Exercise for the reader: the class M of Megido ("Almighty-element") spells, from the Persona series, does have a uniform coefficient of effectiveness of 1 for all targets — even those with Makarakarn (the Shin Megami Tensei equivalent of Reflect) cast on them. Is M⊆N?

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(Edit 2009-02-19: fixed equivalency condition. I think.)