The question of the desirable properties and proper definitions of the Order-of-Magnitude symbols, in particular 0 and e, is addressed once more. The definitions proposed are chosen for complementary mathemati-cal properties, rather than for similarity of form. L brmoDuCTioN The old order changeth, yielding place to new, And God Urals himself in many ways, Lest owe good custom should corrupt thc world-Tennyson, The 14 Ih i f t h e K i n g. The issue of the proper definitions for the Order-of-Magnitude symbols would appear to have been settled once and for all by Knuth in 111. At the end of an exhaustive discussion the subject is, the author feels, about "beaten to death". The purpose of this communica-tion is to point out that there is life in the old dog yeti ' The dehlerations below Were prompted by surprise that, while proving a lower bound where the precise definitions mat-tered, matters % P ere n o t a s d e a r c u t a s o n e m i g h t a s s u m e t h

We consider sequences f: N − → R or f: N − → N or sometimes functions f: R+ − → R. Here N denotes the positive integers, R the real numbers, and R+ the positive real numbers. For asymptotics, we are interested only in the behavior of f(n) for large values of n, so we need only that f be defined for n> k for some k. Asymptotic Relations Often, but not always, we use the following relations in comparing functions f(n) and g(n) that both approach infinity as n approaches infinity. Here are two equivalent notations that say that f(n) grows more slowly than g(n): f(n) ≺ g(n) if and only if f(n) = o(g(n)) if and only if lim n→∞ f(n) g(n) = 0. The second notation, o(g(n)), is Landau’s “little oh ” notation. For example, if 0 < p < q and b> 1, log n ≺ np ≺ nq ≺ bn. Here is how we denote that f(n) and g(n) have the same rate of growth: f(n) ≍ g(n) if and only if |f(n) | ≤ C|g(n) | and |g(n) | ≤ C|f(n)| for some C and all n> some k. A stronger relation says that “f(n) is asymptotic to g(n)”: f(n) ∼ g(n) if and only if lim n→∞ f(n) g(n) = 1. For example, n3 ≍ n3 and n3 ∼ n3

Most of us have gotten accustomed to the idea of using the notation O(f(n)) to stand for any function whose magnitude is upper-bounded by a constant times f(n) , for all large n. Sometimes we also need a corresponding notation for lower-bounded functions, i.e., those functions which are at least as large as a constant times f(n) for all large n. Unfortunately ~ people have occasionally been using the O-notation for lower bounds, for example when they reject a particular sorting method "because its running time is O(n 2) " I have seen instances of this in print quite of tent and finally it has prompted me to sit down and write a Letter to the Editor about the situation. The classical literature does have a notation for functions that are bounded below, namely ~(f(n)). The most prominent appearance of this notation is in Titchmarsh's magnum opus on Riemann's zeta function [8], where he defines ~(f(n)) on p. 152 and devotes his entire Chapter 8 to " ~-theorems". See also Karl Prachar's Primzahlverteilung [7], P. 245.

and creativity have in common, and to show how the topic ofcreativity has been important to personality psychologists and can be to social psychologists. A common system of personality description was obtained by classifying trait terms or scales onto one of the Five-Factor Model (or Big Five) dimensions

g that any constant factor will eventually be overcome. Similarly, if h = !(f ), then h grows faster than f . We say that g is "little-oh" of f , and h is "little-omega" of f . Unlike Big-Oh and Big-Omega, these two sets can be defined exactly in terms of limits. In particular

means, there is still a debate as to whether this should be done with ”big ” or ”little ” architectures. While this subject has typically been approached from the perspective of performance or power, we choose to analyze it in the light of reliability. In recent years reliability has joined performance

set generator with optimal seed length that outputs s\Omega (1) bits when given a function that requires circuits of size s (for any s). This implies a hardness versus randomness tradeoff for RP and BP P that is optimal (up to polynomial factors), solving an open problem raised by [14]. Our generators

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for the individual's overall competence in action, for the individual's inclination toward planful versus impulsive action and for the degree to which the individual's actions are organized by and reflected in the self-concept. Some people think they can do big things. They set out to write a book

with time too. This is the cause of the red shift (it is an alternative to the expansion of the Universe interpretation, and explains the BIG BANG model approach as an apparent interpretation of the observers). The speed of light turns out to be decreasing also with time. An “absolute ” cosmological model