Last Updated：2022/12/24
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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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.
