Possible inconsistent error for "+=" shorthand while using immutable set

Hello,

I'm just starting to learn Scala, and I came across the following example 
in the "Programming in Scala" book.

var jetSet = Set("Boeing", "Airbus")
jetSet += "Lear"
println(jetSet.contains("Cessna"))

One of the lesson points is that the default Set is immutable. So, I wanted 
to test that line 2 in the above actually reassigns a new immutable set 
with the element added to the jetSet variable.

I then *changed the var to a val* and expected to see a reassignment error. 
Instead I got the below error.

immutableSet.scala:2: error: value += is not a member of scala.collection.
immutable.Set[String]
jetSet += "Lear"
       ^

While the error message is true, it's strange that the compiler didn't 
complain about "+=" before. "+=" is shorthand for `jetSet = jetSet + 
"Lear"`, so I would expect to see a reassignment error.

E.g. If I were to run the program with the long form, I get the expected 
error message.

val jetSet = Set("Boeing", "Airbus")
jetSet = jetSet + "Lear"
println(jetSet.contains("Cessna"))

immutableSet.scala:2: error: reassignment to val
jetSet = jetSet + "Lear"
       ^

Am I missing something (very likely since I'm a newb) or does this seem 
inconsistent?

Thanks for reading!
Chris

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