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APPENDIX A
PRINCIPAL CLASSES OF
FUNCTIONS AND SETS
N is the set of all nonnegative integers. x is max(x).
MF is the set of all functions whose domain is a subset of
some N
k
and whose range is a subset of N.
SD is the set of all f
∈
MF such that for all x
∈
dom(f),
f(x) > x.
EVSD is the set of all f
∈
MF such that for all but
finitely many x
∈
dom(f), f(x) > x.
ELG is the set of all f
∈
MF such that there exist c,d > 1
obeying the following condition. For all but finitely many
x
∈
dom(f), cx
≤
f(x)
≤
dx.
LB is the set of all f
∈
MF such that there exists d
obeying the following condition. For all x
∈
dom(f), x
≤
dx.
EXPN is the set of all f
∈
MF such that there exists c > 1
obeying the following condition. For all but finitely many
x
∈
dom(f), cx
≤
f(x).
BAF is the set of all f
∈
MF which can be written using
0,1,+,,•,
↑
,log, where xy = max(xy,0), x
↑
= 2
x
, log(x) =
floor(log(x)) if x > 0; 0 otherwise. Closure under
definition by cases, using <,=, is derived in section 5.1.
INF is the set of all infinite subsets of N.
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 Fall '08
 JOSHUA
 Math, Integers, Sets

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