Compact: Fill & Download for Free

Terminators are supposed to be infiltrators. The entire point of Terminators is that they can get close to specific targets and kill them.The T-800 is an early version of the Terminator. It’s a big, bulky endoskeleton that made for a big, bulky human. The kind of human that you would assume would be a killer machine. Arnold Schwarzenegger is many things, but he is not inconspicuous. The T-800s were an advancement on the T-600s which used rubber skin, but even with real flesh, the T-800s were still very noticeable for just how big they were.As the Terminator program became more advanced, the endoskeletons were able to be made more compact. The more compact they were, the better they were for infiltration. And making them more compact didn’t, in any way, decrease their strength or speed.And with more compact endoskeletons, Skynet began to make Terminators that resembled female humans. Such as the T-X.Or the T-900.These Terminators were much better designed for the original intent of the Terminators: infiltration.

I frequently must use parking garages. There are spaces labeled “Compact.” Sometimes a frickin’ SUV will park in one of those spaces. They leave so little room in the next space that they figure nobody can park there, and they will get the use of two compact parking spaces for their massive vehicle.No problem. I have a smart car; I can park in a mailbox. I can get in there just fine, centered in the space, with room to open my door.I have no sympathy whatsoever for the guy next to me. I will park right on his door. I’m not being the asshole; I have a compact car in a compact space. The asshole is the guy that can no longer get in his improperly parked land barge. His problems are his own damn fault.

As far as I'm aware there is no notion of "compactness" for general sets. I'm guessing you are referring to compact sets in a topological (or metric) space.Intuitively, a compact set is one which is not "too big" and is also "closed" in the sense that it doesn't get infinitely close to any point outside of it.In a topological space, a compact set is a set with the following property: whenever you have a cover of your set by open sets, you can eliminate most of those sets and keep just finitely many of them while still having them cover your original set.This may sound a little confusing.First off, what are "open" sets? Well, if you know what a topological space is, then you know that they come equipped with this notion. Some sets in a topological space are open, some aren't.Intuitively, you can think of open sets as balls (or circles) including their interior but without the boundary. In a metric space, open sets are precisely unions of such balls. For the purposes of defining compact sets in a metric space, it's fine to just consider covers by open balls.(if you don't know what a metric space is, think about the plane or 3d space with the usual notion of distance. An open ball is just the set of points that are at a distance less than R from some point).For example, a square in the plane - including its interior points *and* its boundary - is a compact set. If you cover it by however many open balls, you'll find that you actually don't need more than finitely many of them. This isn't at all obvious but it can be proven (fodder for a separate question).On the other hand, an *open* ball in the plane is not compact. Take the set of points that are at a distance strictly less than 1 from the origin (or whatever fixed point you pick).This set can easily be covered with finitely many open balls - in fact, you need just one: itself! But it also admits covers with infinitely many sets that cannot be reduced to finitely many ones. For example, take the ball of radius 1/2 around the same center, and the ball of radius 2/3, and then radius 3/4, then 4/5 and so on.These infinitely many balls cover the original open ball of radius 1 completely: any point in the large ball belongs to one of the smaller balls. But you cannot achieve that by keeping just finitely many small balls.Thus: a closed ball, or a closed square, are compact. An open ball, or the whole plane, are not.--There is also a notion of compactness in logic, which is in some sense equivalent to the topological notion. I don't think this is what you're asking about though.