Why is BigDecimal natural ordering inconsistent with equals?

Question

From the Javadoc for BigDecimal:

Note: care should be exercised if BigDecimal objects are used as keys in a SortedMap or ele

Answer 1

From the OpenJDK implementation of BigDecimal:

/**
     * Compares this {@code BigDecimal} with the specified
     * {@code Object} for equality.  Unlike {@link
     * #compareTo(BigDecimal) compareTo}, this method considers two
     * {@code BigDecimal} objects equal only if they are equal in
     * value and scale (thus 2.0 is not equal to 2.00 when compared by
     * this method).
     *
     * @param  x {@code Object} to which this {@code BigDecimal} is 
     *         to be compared.
     * @return {@code true} if and only if the specified {@code Object} is a
     *         {@code BigDecimal} whose value and scale are equal to this 
     *         {@code BigDecimal}'s.
     * @see    #compareTo(java.math.BigDecimal)
     * @see    #hashCode
     */
    @Override
    public boolean equals(Object x) {
        if (!(x instanceof BigDecimal))
            return false;
        BigDecimal xDec = (BigDecimal) x;
        if (x == this)
            return true;
    if (scale != xDec.scale)
        return false;
        long s = this.intCompact;
        long xs = xDec.intCompact;
        if (s != INFLATED) {
            if (xs == INFLATED)
                xs = compactValFor(xDec.intVal);
            return xs == s;
        } else if (xs != INFLATED)
            return xs == compactValFor(this.intVal);

        return this.inflate().equals(xDec.inflate());
    }

More from the implementation:

 * 
Since the same numerical value can have different
 * representations (with different scales), the rules of arithmetic
 * and rounding must specify both the numerical result and the scale
 * used in the result's representation.

Which is why the implementation of equals takes scale into consideration. The constructor that takes a string as a parameter is implemented like this:

    public BigDecimal(String val) {
        this(val.toCharArray(), 0, val.length());
    }

where the third parameter will be used for the scale (in another constructor) which is why the strings 1.0 and 1.00 will create different BigDecimals (with different scales).

From Effective Java By Joshua Bloch:

The final paragraph of the compareTo contract, which is a strong suggestion rather than a true provision, simply states that the equality test imposed by the compareTo method should generally return the same results as the equals method. If this provision is obeyed, the ordering imposed by the compareTo method is said to be consistent with equals. If it’s violated, the ordering is said to be inconsistent with equals. A class whose compareTo method imposes an order that is inconsistent with equals will still work, but sorted collections containing elements of the class may not obey the general contract of the appropriate collection interfaces (Collection, Set, or Map). This is because the general contracts for these interfaces are defined in terms of the equals method, but sorted collections use the equality test imposed by compareTo in place of equals. It is not a catastrophe if this happens, but it’s something to be aware of.