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2Tupel

2Tupel, also called a two-tuple or ordered pair, is a basic mathematical object consisting of two elements arranged in a specific order. The first component and the second component may come from the same set or from different sets, and the order of the components matters.

Notation and formal definition: If A and B are sets, a 2Tupel is an element of the

View as functions and set constructions: A 2Tupel can be viewed as a function f: {1, 2}

Relation to higher arity: A 2Tupel is the simplest nontrivial tuple (also called a binary tuple). It

Applications and examples: In geometry, coordinates of a point in the plane are a 2Tupel (x, y).

See also: 3-tuple, Cartesian product, ordered pair, Kuratowski definition.

Cartesian
product
A
×
B.
If
the
components
come
from
the
same
set
X,
the
2Tupel
is
an
element
of
X
×
X.
A
2Tupel
is
typically
written
as
(a,
b)
or
⟨a,
b⟩,
with
the
convention
that
(a,
b)
=
(c,
d)
if
and
only
if
a
=
c
and
b
=
d.
→
X
where
f(1)
=
a
and
f(2)
=
b,
often
used
to
model
ordered
data.
In
set-theoretic
constructions,
the
Kuratowski
definition
represents
(a,
b)
as
{{a},
{a,
b}}
to
encode
order
using
sets.
contrasts
with
a
set
of
two
elements,
where
order
and
multiplicity
are
not
generally
meaningful.
Higher-order
tuples
generalize
the
idea
to
three
or
more
components.
In
programming,
a
pair
type
stores
two
values,
possibly
of
different
types.
In
databases
and
data
exchange,
2Tupel-like
records
capture
two
related
fields,
such
as
a
key
and
a
value.