flatMap is simply flatten compose map

imaging when you

1. map an Array [1,2,3] with function x=>[x], you'll get [[1],[2],[3]]
2. flatten will flatten the nested array into a flat array [1,2,3]

same thing happen to Stream

1. map --1--2--3--> with function x=>Stream(x+1) will return --S(1+1)--S(2+1)--S(3+1)-->
2. so if S(1+1) represent as --2-->, flatten will flatten the nested Stream into flat Stream ----2----3----4-->

ref to Notation if these symbols make no sense to you.