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Comment by HelloNurse | Hacker News Reader

Numbers are not "conditionally" finite or constant. Either you know their value or you don't.

In this specific case, "the number of variations of code", "any computing language in existence" and "the behavior of the game Doom including the game’s initial creation" are three separate vague concepts that can only be formalized in complex and arbitrary ways.

If you did, however, you would find yourself on the familiar ground of enumerating "programs" (or something similar, like Turing machines or Gödel numbers) and considering predicates about them. This means dealing exclusively with integers, speaking of irrational numbers doesn't make sense in this context.

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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.

> Imaginary number is irrational

I don't think that's the case. `i` is not irrational, it's just perpendicular to 1.

Yes, i is neither rational nor irrational. I just edited to correct/remove that.

It’s possible that I cannot define an irrational number as an real number member in a sometimes unknown location within a result set of a function, where the size of the set being exactly one results in the possibility of the number being known exactly.

But it has a lot in common with irrational numbers, aside from it looking to meet the qualifications of being irrational.

If you assume total omniscience, then the result of the function would always result in a real, rational number, and that is the number I’m trying to define as irrational, because the answer as defined is always an integer, but depending on the values of the parameters to the function, which number it is would be unknown, and that cannot be defined as a fraction.

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