esoter

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.

A word of warning: you’ll have to browse or crawl these pages periodically at minimum.

Best case would be to diff the latest page with various IPs and user-agents against the known and then let you know when it changes. Someone will inevitably submit a page that looks good, then changes later or dynamically depending on datetime, user-agent, request IP, etc. to become malicious.

Unfortunately, these are the sorts of problems that many companies have to deal with automatically (like Google) or manually that startups don’t typically.

While you’re charging, if someone can get by with paying $1 for installing ransomware, they may do it.

It’s a neat idea, but it’s risky. I like what you’ve done, though, and hope the artisanal webpage index pays for itself and more quickly.

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.

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.

I’m proposing a new irrational number.

It’s sometimes constant and sometimes not, depending on conditions, but is a set of finite numbers, where that set may be of unknown length or may be a known set of a single number.

It’s a real number as it could be plotted, but is not definable as a fraction, as conditionally it could be of unknown set length.