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

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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<X> 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)

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