In this case, the function in the example representing a Doom value is a definite value in the set resulting from f(d, o), where d is the current date, and omniscience is o. Where the date of Doom game creation is t, when d ~< t, Doom is 0. Otherwise, the result from f(d, o) is either a set containing a single possible integer solution if o is high or a set of an unknown number of possible integer solutions if o is low, with the length of that set also being dependent on proximity of d to t.

Doom is a real number under any circumstance as there is only one value it can be of the set produced by f(d, o) and that value is a real number.

Doom cannot always be represented by a fraction, because it is an indeterminate constant when d is higher than t and o is not high.