A Note on Notation

Some of the symbolism in this book has not (yet?) become standard. Here is a list of notations that might be unfamiliar to readers who have learned similar material from other books, together with the page numbers where these notations are explained. (See the general index, at the end of the book, for references to more standard notations.)

Notation	Name	Page
ln x	natural logarithm: loge x	276
lg x	binary logarithm: log2 x	70
log x	common logarithm: log10 x	449
x	floor: max{ n | n ≤ x, integer n }	67
x	ceiling: min{ n | n ≥ x, integer n }	67
x mod y	remainder: x – yx/y	82
{x}	fractional part: x mod 1	70
	indefinite summation	48
	definite summation	49
xn	falling factorial power: x!/(x – n)!	47, 211
	rising factorial power: Γ(x + n)/Γ(x)	48, 211
n¡	subfactorial: n!/0! – n!/1! + · · · + (–1)nn!/n!	194
ℜz	real part: x, if z = x + iy	64
ℑz	imaginary part: y, if z = x + iy	64
Hn	harmonic number: 1/1 + · · · + 1/n	29
	generalized harmonic number: 1/1x + · · · + 1/nx	277
f(m)(z)	mth derivative of f at z	470
	Stirling cycle number (the “first kind”)	259
	Stirling subset number (the “second kind”)	258
	Eulerian number	267
	Second-order Eulerian number	270
(am . . . a0)b	radix notation for	11
K(a1, . . . , an)	continuant polynomial	302
	hypergeometric function	205
#A	cardinality: number of elements in the set A	39
[zn] f(z)	coefficient of zn in f(z)	197
[α . . β]	closed interval: the set {x | α ≤ x ≤ β}	73
[m = n]	1 if m = n, otherwise 0*	24
[mn]	1 if m divides n, otherwise 0*	102
[m\n]	1 if m exactly divides n, otherwise 0*	146
[m ⊥ n]	1 if m is relatively prime to n, otherwise 0*	115

If you don’t understand what the x denotes at the bottom of this page, try asking your Latin professor instead of your math professor.

Prestressed concrete mathematics is concrete mathematics that’s preceded by a bewildering list of notations.

Also ‘nonstring’ is a string.

*In general, if S is any statement that can be true or false, the bracketed notation [S] stands for 1 if S is true, 0 otherwise.

Throughout this text, we use single-quote marks (‘. . . ’) to delimit text as it is written, double-quote marks (“. . . ”) for a phrase as it is spoken. Thus, the string of letters ‘string’ is sometimes called a “string.”

An expression of the form ‘a/bc’ means the same as ‘a/(bc)’. Moreover, log x/log y = (log x)/(log y) and 2n! = 2(n!).