Watsisname wrote:If the numbers loop back to negative, then you haven't gone high enough. To illustrate with y=tan(x), that means you stepped too far in x, and thus missed a bunch of y. In fact you did not just miss a bunch, but an infinite amount of it. Get closer and closer to that singularity, and you move through ever vaster amounts of y for ever smaller amounts of x.
Singularities are fun.
Wat, I wish I could find the article, I read it years ago (something like 10 years ago) and it went into great detail explaining all the different types of numbers, going into rational, irrational, transcendental, imaginary, complex, and some other types I did not even know existed and it posited the idea of a circular number system and ever since then I've been intrigued by it as a roadmap for a mathematical omniverse. It does remind me of the tangent function and how it's graphed..... The asymptotes of the function you mentioned are that which is never reached, but instead approached and then restarted back "on the other side" at the lowest level. It also reminded of the idea that a luxon wall (where everything travels at the speed of light) separates two universes that are tachyonic relative to one another (they have opposite arrows of time relative to the other but both are forward relative to everything inside each- think of two conveyor belts going in different directions, but both go forward relative to what is on each belt.) Then we had the two universe theory that came out in 2013 that seemed to mirror that (including expansion/contracting cycles that kept the two in balance); If you attempted to go from one universe to the other (it was specifically stated you could not do so directly) adding momentum would actually decrease speed towards the speed of light asymptote. Below absolute zero temperatures can be thought of the same way. It is absolute zero which can never be reached, but as an asymptote, the concept of below absolute zero temperatures are still possible (and actually something that has been measured- and just like with the above analogy, the more heat you add, the lower the temperature gets, and as you take it away the temperature rises towards the absolute zero asymptote.)
Asymptotes-Limits-Singularities= fascinating stuff!