In this case it can, but only conditionally. At all times, with sufficient knowledge and defined state you could instantaneously determine the Doom value, so i

In this case it can, but only conditionally. At all times, with sufficient knowledge and defined state you could instantaneously determine the Doom value, so it is a real number. With the example, prior to creation of the game Doom, Doom value would be 0. Around the point of creation, the value would probably be 1, because prior to that point Doom did not exist, and then it would. After creation, there could be a limit given the available hardware, languages, etc. and code for Doom in those languages. A large number of variations of the code in various languages could still produce Doom. Given sufficient knowledge, there could be a finite value of Doom. But practically if we had to feed an actual set of numbers that could equal Doom into a machine given what we could ascertain, it would be a finite set. In our example, since there exists a defined value for Doom, it is real. Since that defined value can only conditionally be known, and otherwise is a set of unknown length, it is conditionally not a constant that is representable by a fraction.