In Stream reduce method, must the identity always be 0 for sum and 1 for multiplication?

Question

I proceed with java 8 learning.

I have found an interesting behavior:

let\'s see code sample:

// identity value and accumulator and combiner         


        

Answer 1

The identity value is a value, such that x op identity = x. This is a concept which is not unique to Java Streams, see for example on Wikipedia.

It lists some examples of identity elements, some of them can be directly expressed in Java code, e.g.

• reduce("", String::concat)
• reduce(true, (a,b) -> a&&b)
• reduce(false, (a,b) -> a||b)
• reduce(Collections.emptySet(), (a,b)->{ Set s=new HashSet<>(a); s.addAll(b); return s; })
• reduce(Double.POSITIVE_INFINITY, Math::min)
• reduce(Double.NEGATIVE_INFINITY, Math::max)

It should be clear that the expression x + y == x for arbitrary x can only be fulfilled when y==0, thus 0 is the identity element for the addition. Similarly, 1 is the identity element for the multiplication.

More complex examples are

• Reducing a stream of predicates

  reduce(x->true, Predicate::and)
  reduce(x->false, Predicate::or)
  

• Reducing a stream of functions

  reduce(Function.identity(), Function::andThen)