It may help you to read Introduction to Algebra first. An equation says that two things are equal. It will have an equals sign = like this: That equation says: what is on the left (x + 2) is equal to what is on the right (6) So an equation is like a statement this equals that.
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I hear that YouTube is, or will soon support some sort of live stream, so Apple TV could conceivably support that. Once apps start coming onto Apple TV some live TV app may appear (assuming apps DO appear one day). As for 1080p, yes it doesn't have it. But the Apple TV 720p streams look better on my Pioneer Kuro than the DirecTV 1080p pay per view feeds, I believe. Or at the least, they looks essentially the same.