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The general usage contract for {{compareTo()}} from Java SE 6 API \[[API 2006|AA. Bibliography#API 06]\] (numbering added) states that

1. The implementor must ensure sgn(x.compareTo(y)) == -sgn(y.compareTo(x)) for all x and y. (This implies that x.compareTo(y) must throw an exception iff y.compareTo(x) throws an exception.)

2. The implementor must also ensure that the relation is transitive: (x.compareTo(y) > 0 && y.compareTo(z) > 0) implies x.compareTo(z) > 0.

3. Finally, the implementor must ensure that x.compareTo(y) == 0 implies that sgn(x.compareTo(z)) == sgn(y.compareTo(z)), for all z.

4. It is strongly recommended, but not strictly required that (x.compareTo(y) == 0) == x.equals(y). Generally speaking, any class that implements the Comparable interface and violates this condition should clearly indicate this fact. The recommended language is "Note: this class has a natural ordering that is inconsistent with equals."

In the foregoing description, the notation sgn(expression) designates the mathematical signum function, which is defined to return either -1, 0, or 1 depending on whether the value of the expression is negative, zero or positive.

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However, this game violates the notion of transitivity, since because Rock beats Scissors, Scissors beats Paper, but Rock does not beat Paper.

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