Many would defend utility theory (as well as other aspects of their standard model of behaviour) as a useful approximation, pointing out that exceptions to approximations can always be found.
Note that we could also use the straight line r nj r mj to do the approximation, but simulations demonstrate that the r nj ′ r Mj ′ approximation is always better than r nj r mj.
Various simple methods of approximation will always yield the same succession of digits in the same order.
Determined social movements against what seemed to be fixed features of social life often work to a first approximation, they always work, which is why the modern history of liberal societies has the generally happy arc it does.
Although an MO can in principle be determined by solving the Schrödinger equation for an electron in the electrostatic field of an array of nuclei, in practice an approximation is always adopted.
Determined social movements against what seemed to be fixed features of social life often work — to a first approximation, they always work, which is why the modern history of liberal societies has the generally happy arc it does.
And that Shakespeare was good-looking as a young man, before he lost his hair and puffed out from home-cooking, seems at least likely, on the fixed general principle that writers who become very celebrated in their youth, as he did, are, to a first approximation, almost always good-looking.
Corollary 1 implies that, if μ n ∼ E X n , then the Poisson approximation will always overestimate the exact probability as n→∞.
The Fermi integral with Maxwellian approximation is always an exponential for all values of i and is given by ℑ i η F ≈ e η nondegenerate (11).
Knowledge and skills are always approximations.
