First of all, I am not really sure wether I have posted this topic in the right section of the forum. If not, moderators, please move this topic to the correct forum :-).
I'm not from a country where English is the native language, so especially with more specific subjects such as math I'm having trouble understanding everything. One of these things is the use of "arbitrarily", which appears to have the meaning "limitless/with no limit, but still finite". I am wondering: how can something be limitless but not infinite, as it's finite?
Besides that, I'm working on an essay which is about chaos theory, and I have come accross a definition which states a set M (by a dynamical system) whose elements are the same as N's or come arbitrarily close to it, which is defined as dense orbits. What does arbitrarily mean in this sense, and how could I get "arbitrarily" into an equation (what symbol would be used aswell)?