Last Updated：2025/12/30
Sentence
This
one-to-one
correspondence
between
the
set
of
positive
integers
and
the
set
of
pairs
of
positive
integers
indicates
that
the
set
of
pairs
is
countably
infinite.
Since
the
set
of
positive
rational
numbers
is
a
subset
of
the
set
of
all
pairs
of
positive
integers,
the
set
of
positive
rational
numbers
is
at
most
countably
infinite.
Then,
since
it
is
also
at
least
countably
infinite,
the
set
of
positive
rational
numbers
is
countably
infinite.
Quizzes for review
This one-to-one correspondence between the set of positive integers and the set of pairs of positive integers indicates that the set of pairs is countably infinite. Since the set of positive rational numbers is a subset of the set of all pairs of positive integers, the set of positive rational numbers is at most countably infinite. Then, since it is also at least countably infinite, the set of positive rational numbers is countably infinite.
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English - English
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