let setFromArray: Set = [ 1, 2, 4, 5] works because Set conforms to ExpressibleByArrayLiteral and hence has an initializer that takes an ArrayLiteral. See Set.init(arrayLiteral:). This conformance gives syntactic sugar for not having to explicitly call the init.

On the other hand, once you save the array literal into a variable using let elements = [ 1, 2, 3, 4, 5, 1, 2, 6, 7], elements becomes an Array, not an ArrayLiteral and hence another initializer of Set has to be called that takes an Array. This init does not provide syntactic sugar like ExpressibleByArrayLiteral does, so you explicitly have to call the init by doing Set(array).

The getting and setting of variables within classes refers to either retrieving ("getting") or altering ("setting") their contents.

Consider a variable members of a class family. Naturally, this variable would need to be an integer, since a family can never consist of two point something people.

So you would probably go ahead by defining the members variable like this:

class family {
    var members: Int
}

This, however, will give people using this class the possibility to set the number of family members to something like 0 or 1. And since there is no such thing as a family of 1 or 0, this is quite unfortunate.

This is where the getters and setters come in. This way you can decide for yourself how variables can be altered and what values they can receive, as well as deciding what content they return.

Returning to our family class, let's make sure nobody can set the members value to anything less than 2:

class family {
    var _members: Int = 2
    var members: Int {
      get {
        return _members
      }
      set (newVal) {
        if newVal >= 2 {
          _members = newVal
        } else {
          println('error: cannot have family with less than 2 members')
      }
    }
  }
}

Now we can access the members variable as before, by typing instanceOfFamily.members, and thanks to the setter function, we can also set it's value as before, by typing, for example: instanceOfFamily.members = 3. What has changed, however, is the fact that we cannot set this variable to anything smaller than 2 anymore.

Note the introduction of the _members variable, which is the actual variable to store the value that we set through the members setter function. The original members has now become a computed property, meaning that it only acts as an interface to deal with our actual variable.