Why are these == but not `equals()`?

Question

I\'m a bit confused about the way Java treats == and equals() when it comes to int, Integer and other types of numbers.

Answer 1

(small) Integer instances are cached, so the invariant x == y is holded for small instances (actually -127 +128, depends on JVM):

Integer a = 10;
Integer b = 10;

assert(a == b); // ok, same instance reused

a = 1024;
b = 1024;

assert(a == b); // fail, not the same instance....
assert(a.equals(b)); // but same _value_

EDIT

4) and 5) yield false because equals check types: X is an Integer whereas Y is a Short. This is the java.lang.Integer#equals method:

public boolean equals(Object obj) {
    if (obj instanceof Integer) {
        return value == ((Integer)obj).intValue();
    }

    return false;
}