"Ordinary sums like 9 x 7 are for the lesser mechanical mortals.
One is focused on the ordinary sums, and the other is concerned with the square sums.
Moreover, if its ordinary partial sums (1) is univalent in U, then the Cesáro sums are univalent.
It is trivial that (S_{n} le S) and that the sequence of ordinary partial sums ({x_{1} + cdots+ x_{n}}) is non-decreasing.
Next, we assume special ordinary partial sums depending so that their coefficients satisfy the relation | a n | ≤ ( k − n + 1 k ).
When applied to infinite-dimensional modal boundary discontinuities, the method of orthocomplement eliminates the Gibbs oscillations that affect the ordinary spectral sums, and produces the same corrected formulae as it did for finite-dimensional examples.
Remark 4 In view of Theorem 3, for example, the values α = 0.5, k = 2 and | a k | = 1 pose the radius of convexity of S k ( z ) is r = 0.577350 … and for the same values, the radius of convexity of the ordinary partial sums f k ( z ) = z + a k z k is r = 0.4082 … (see [2]).
Remark 2 For example, the values α = 0.5, k = 2 and | a k | = 1 imply the radius of starlikeness of S k ( z ) is r = 0.8164965 … , and for the same values, the radius of starlikeness of the ordinary partial sums f k ( z ) = z + a k z k is r = 0.577350 … (see [2]).
If one is a realist about both ordinary objects and sums, and takes parsimony about ontological categories seriously, then coincidentalism is an appealing position.
While both ordinary objects and sums (which are also objects) exist, they cannot be identical, since the clay can both pre-exist the statue it constitutes, and can survive past the statue being crushed.
