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In the early part of this century, French mathematician Paul Levy explored these possibilities and discovered a class of random walks in which the steps vary in size, from infinitesimally small to infinitely large, so no average or characteristic length can be calculated.
Indeed, in its broadest mathematical sense, chaos imposes one key requirement: that a system with a given set of initial conditions, such as a particular value for its starting position and momentum, will evolve far differently than the same system with a set of initial conditions varying only infinitesimally from the first.
The idea is that no matter where you are, if you step infinitesimally to one side, you could fall into one of the holes, meaning you could end up at a completely different attractor.
So you went from having to show something was actually about to happen to the likelihood that something increased even infinitesimally," he said.
Cited in the cable, Ahmar bragged to an economic official from the US Embassy that he earned $50,000 per month from Arcadia, but the amount was "an infinitesimally marginal part of my income".
Finance for SMEs Companies in the Middle East are gradually realising the value of credit insurance, but the percentage of trade covered by such insurance is infinitesimally small, according to trade related credit insurance solutions provider Euler Hermes.
The chance of getting this one right is infinitesimally small.
The chances that it wouldn't have disintegrated prior to fossilization were infinitesimally small.
The book is unique for its presentation of a new theory for the tangential and normal derivatives of flow properties (such as pressure and velocity) just downstream of an infinitesimally thin, curved shock wave.
Perhaps my favorite example is when, in the footnotes, O'Brien's (fictional) philosopher de Selby explains how the picture you see of yourself in the mirror is, in fact, an infinitesimally younger version of yourself, given the speed of light: If mirrored enough, you would in theory see yourself as a child.
Many years ago when I was carrying out electrical ground tests at the then Llanelli power station there were two (if memory serves me correctly) relatively small wind generators on site, which when enquired about, were regarded simply as 'toys-for-boys' and I would suggest the only difference these days is that the toys have got very much bigger, although unfortunately at the expense of countryside degradation, devaluation of property, threat to health, slaughter of both bats and birdlife, infinitesimally small reduction in UK carbon emissions as to be absolutely laughable on a planetary scale, and last but not least, no security of supply