Last Updated：2025/12/30
Sentence
If
an
ordered
pair
were
defined
(in
terms
of
sets)
as
(x,y):=a,a,b
then
the
"first
element"
of
an
ordered
pair
S
could
be
defined
as
CAR(S)
where
CAR(S)
=
x
if
and
only
if
(∀y∈S.,x∈y).
Likewise,
the
"second
element"
of
S
could
be
defined
as
CDR(S)
where
CDR(S)
=
x
if
and
only
if
(∃y∈S.,(∃z∈y.,x∈z)).
If
the
two
elements
happened
to
be
equal,
then
the
ordered
pair
would
still
have
cardinality
two
as
would
be
naturally
expected.
Quizzes for review
If an ordered pair were defined (in terms of sets) as (x,y):=a,a,b then the first element
of an ordered pair S could be defined as CAR(S) where CAR(S) = x if and only if (∀y∈S.,x∈y). Likewise, the second element
of S could be defined as CDR(S) where CDR(S) = x if and only if (∃y∈S.,(∃z∈y.,x∈z)). If the two elements happened to be equal, then the ordered pair would still have cardinality two as would be naturally expected.
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English - English
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