The final formulation was a discrete model with infinite terms.
The proposed procedure uses infinite terms of high-order polynomial to describe the uneven longitudinal displacement in the flanges.
In addition, the underlying Gaussian random field is often generated by series expansion approaches (e.g. spectral representation method), which require a sum of infinite terms.
Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving, at any order, certain symmetries of the exact solution.
Since the formulae involve sums of infinite terms and integrations along the entire wavenumber-axis, truncations must be made.
However, in view of (1), (T^{n}x) has infinite terms lying in each (A_{i}), (iin { 1,2,ldots,p }).
So although William holds that the same thing is signified, the mode of signification would preclude substitution of positive and infinite terms.
Since these terms are not finite, they cannot be made infinite: "Terms that contain all things cannot be made infinite, hence this is senseless: 'a non-something is', 'a non-thing is'".
Many physicists tried to avoid the divergences by formal tricks (truncating the integrals at some value of momentum, or even ignoring infinite terms) but such rules were not reliable, violated the requirements of relativity and were not considered as satisfactory.
