Subject Index
Bold page numbers refer to chapters (153–173)or
to sections (
148
), with the chapter page numbers
a bit larger; italicized page numbers (
186
) refer to
definitions of mathematical terms; and typewriter
font page numbers (
116
) refer to exercises.
Aha! moments .................xiii, xiv, 57, 112
algebraic numbers ...........................3
anthropomorphization ...............43,55,160
arithmetic progression ...................... 23
axiomatic development ....................xvii
axiom of choice ...........................149
back-and-forth argument ...................170
back-propagation method ....................85
Bezout’s identity ........................... 20
bijective function ......................... 129
binary relation ............................121
binary representation ........................33
binomial square ............................58
Bolzano-Weierstrass theorem ...............181
Cantor, Georg ...........................3,150
Cantor’s cruise ship .....................146
diagonal argument ......................151
Q is universal ..........................168
R is uncountable ...................150, 152
Shr
¨
oder-Cantor-Bernstein ...............157
and transcendental numbers ............. 154
chocolate bar problems .......... 43, 56, 81, 90
n choose k .................................50
circuit, in a graph ..........................134
classical beginning ........................
1–8
cluster point ..............................181
combinatorial game theory .................. 88
commensurable numbers .....................1
complex numbers ............................3
composition of functions ...................129
congruence ...............................124
see also modular arithmetic
constructible proof ........................ 155
continuity ................................
173
at exactly one point .....................
177
epsilon-delta definition .................
174
preserved by sum and product ...........
175
uniform continuity .....................
184
continuous induction principle .........
182
,
186
corollary, meaning of ......................
xxii
countable sets .............................
146
A
∗
is countable .........................150
countable unions .......................149
N × N is countable ......................147
Q is countable ..........................149
union of two countable sets ..............146
Z is countable ..........................147
see also uncountable sets
cranks ....................................153
decreasing sequence .......................181
degree of vertex, in a graph .................135
Dehn, Max ............................... 117
dense order ...............................170
diagonal real number ......................151
discrete mathematics ....................
41–56
dissection congruence theorem ........111–119
see also polygonal dissection theorem
divides relation ............................121
domain of a function .......................128
dominoes ...............28,63, 64, 69, 70, 192
drawing strategy ........................... 85
empty product ..............................18
endless order ..............................170
equinumerosity ...........................156
plane and line are equinumerous .........159
see also countable, uncountable