...102#102.
The notation 103#103 denotes the floor function , which is defined as follows: For any real number x, 104#104 is the greatest integer less than or equal to x. While we are on the subject, there is a related function, the ceiling function , written 105#105. For any real number x, 106#106 is the smallest integer greater than or equal to x. 
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...119#119.
In fact, we would normally write 120#120, but we have not yet seen the 1#1 notation which is introduced in Chapter gif. 
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...rule
Guillaume François Antoine de L'Hôpital, marquis de Sainte-Mesme, is known for his rule for computing limits which states that if 357#357 and 358#358, then

359#359

where f'(n) and g'(n) are the first derivatives with respect to n of f(n) and g(n), respectively. The rule is also effective if 360#360 and 361#361. 

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...commensurate.
Functions which are commensurate  are functions which can be compared one with the other. 
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...436#436.
This notion of the looseness (tightness ) of an asymptotic bound is related to but not exactly the same as that given in Definition gif. 
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...numbers.
Fibonacci numbers are named in honor of Leonardo Pisano (Leonardo of Pisa), the son of Bonaccio (in Latin, Filius Bonaccii), who discovered the series in 1202. 
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...numbers.
These running times were measured on an Intel Pentium III, which has a 1 GHz clock and 256MB RAM under the Red Hat Linux 7.1 operating system. The programs were executed using the Ruby version 1.8.0 interpreter. 
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...class
For a complete list of the methods defined in the Object class, you should consult the Ruby Reference Manual[38]. 
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...NAME=7187> .
The word deque is usually pronounced like ``deck'' and sometimes like ``deek.'' 
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...order
A total order is a relation, say <, defined on a set of elements, say 791#791, with the following properties:
  1. For all pairs of elements 792#792, such that 793#793, exactly one of either i<j or j<i holds. (All elements are commensurate ).
  2. For all triples 794#794, 795#795. (The relation 394#394 is transitive ).

(See also Definition gif). 

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...

819#819

I have been advised that a book with out sex will never be a best seller. ``Sex'' is the Swedish word for the number six. 

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...prime
Two numbers x and y are relatively prime   if there is no number other than one that divides both x and y evenly. 
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...i.
What else would it be? 
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...NAME=14298> .
Isomorphic is a fancy word that means being of identical or similar form or shape or structure. 
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...Landis
Russian mathematicians G. M. Adel'son-Vel'skiı and E. M. Landis published this result in 1962. 
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...trees.
Obviously since B-Trees are M-way trees, the ``B'' in B-Tree does not stand for binary. B-Trees were invented by R. Bayer and E. McCright in 1972, so the ``B'' either stands for balanced or Bayer-take your pick. 
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...HREF="page383.html#exercisepqueuesbinom">gif).
Isaac Newton  discovered the binomial theorem in 1676 but did not publish a proof. Leonhard Euler  attempted a proof in 1774. Karl Friedrich Gauss  produced the first correct proof in 1812. 
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...subsets.
Stirling numbers of the second kind  are given by the formula

1608#1608

where n>0 and 1609#1609. 

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...structures.
Mark-and-sweep garbage collection is described by John McCarthy in a paper on the LISP language published in 1960. 
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...space.
The reader may find it instructive to compare Program gif with Program gif and Program gif. 
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...space.
The reader may find it instructive to compare Program gif with Program gif and Program gif. 
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...NAME=32688> .
The table is named in honor of Blaise Pascal  who published a treatise on the subject in 1653. 
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...number!
Prime numbers of the form 1904#1904 are known as Mersenne primes . 
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...1907#1907.
For convenience, we use the notation 1908#1908 to denote 1909#1909. 
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...NAME=34614> .
Unfortunately, the fame of bubble sort exceeds by far its practical value. 
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...zero.
There is also the symmetrical case in which i is always n-1. 
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...(respectively)
In Ruby the names of instance attributes always begin with an at sign ``@''. 

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Bruno Copyright © 2004 by Bruno R. Preiss, P.Eng. All rights reserved.