The trouble with hashCode in mutable objects

gistfile1.java

import java.util.HashSet;
import java.util.Set;

public class Main {
  
	public static void main(String[] args) {
		Set<Foo> set = new HashSet<Foo>();
		
		Foo apple = new Foo("apple");
		
		set.add(apple);
		set.add(new Foo("apple")); // Don't add duplicate objects
		
		System.out.print("Set is size: " + set.size() + " and contains: ");
		
		for(Foo foo : set) {
			System.out.print(foo.getValue() + " (" + foo.hashCode() + "), ");  
		}
		
		System.out.println("");
		
		apple.setValue("banana");
		set.add(new Foo("banana")); // Shouldn't add a duplicate object, but ...
		
		System.out.print("Set is size: " + set.size() + " and contains: ");		
		
		for(Foo foo : set) {
			System.out.print(foo.getValue() + " (" + foo.hashCode() + "), "); 
		}
	}
}

// POJO value class, nothing strange, autogenerated hashCode and equals
class Foo {

	private String value;

	public Foo(String value) {
		super();
		this.value = value;
	}

	public String getValue() {
		return value;
	}

	public void setValue(String value) {
		this.value = value;
	}

	@Override
	public int hashCode() {
		final int prime = 31;
		int result = 1;
		result = prime * result + ((value == null) ? 0 : value.hashCode());
		return result;
	}

	@Override
	public boolean equals(Object obj) {
		if (this == obj)
			return true;
		if (obj == null)
			return false;
		if (getClass() != obj.getClass())
			return false;
		Foo other = (Foo) obj;
		if (value == null) {
			if (other.value != null)
				return false;
		} else if (!value.equals(other.value))
			return false;
		return true;
	}

}