For each of the following values of S, after spec of S, put <, ~, or > to stand for "S < N", "S ~ N", "S > N". Make them legible! a. S = the set of all integers, positive, negative, and 0 b. S = the reals given by the open interval (10, 11) c. S = { T | T is a subset of { a, b, c } }
Cardinality
1. Using N for the set of nonnegative integers, N = {0, 1,
... },
for a set S we write "S < N" when the cardinality of S is
finite, "S ~ N" when the S is countably infinite, and "S >
N"
when S is uncountable.
For each of the following values of S, after spec of S, put
<, ~,
or > to stand for "S < N", "S ~ N", "S > N". Make them
legible!
a. S = the set of all integers, positive, negative, and 0
b. S = the reals given by the open interval (10, 11)
c. S = { T | T is a subset of { a, b, c } }
d. S = { T | T is a subset of N }
e. S = { q | q is a rational number }
f. S = A* for the finite alphabet A = { 0, 1 }
g. S = { seq | seq is an infinite sequence of bits,
which we might represents as
seq : N -> { 0, 1 } as a function from
N to { 0, 1 } }
h. S = A X B X C for finite sets A, B, and C
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