def METHOD_NAME(self, i):
    r"""
    The default counit of a graded connected Hopf algebra.
    INPUT:
    - ``i`` -- an element of the index set
    OUTPUT:
    - an element of the base ring
    .. MATH::
        c(i) := \begin{cases}
        1 & \hbox{if $i$ indexes the $1$ of the algebra}\\
        0 & \hbox{otherwise}.
        \end{cases}
    EXAMPLES::
        sage: H = GradedHopfAlgebrasWithBasis(QQ).Connected().example()     # needs sage.modules
        sage: H.monomial(4).counit()  # indirect doctest                    # needs sage.modules
        0
        sage: H.monomial(0).counit()  # indirect doctest                    # needs sage.modules
        1
    """
    if i == self.one_basis():
        return self.base_ring().one()
    return self.base_ring().zero()