Home

mengde

Mengde is the Norwegian term for the mathematical concept commonly translated as “set.” A set is a collection of distinct objects, called elements, for which membership is well defined. The order of elements does not matter, and duplicates are not allowed.

In notation, an element a belongs to a set A is written a ∈ A. If every element

Special sets include the empty set ∅, which has no elements. The power set P(A) is the set

Applications of the concept include formal reasoning, counting and probability, and the use of Venn diagrams

of
A
is
also
an
element
of
B,
A
is
a
subset
of
B,
written
A
⊆
B.
The
union
A
∪
B
combines
elements
from
both
sets;
the
intersection
A
∩
B
contains
elements
common
to
both.
The
difference
A
\
B
(or
A
−
B)
contains
elements
in
A
that
are
not
in
B.
The
complement
A^c
(or
A′)
consists
of
elements
not
in
A,
relative
to
a
universal
set
U.
The
cardinality
|A|
counts
the
elements
in
A;
finite
sets
have
finite
cardinalities,
while
infinite
sets
do
not.
of
all
subsets
of
A.
Set-builder
notation
describes
a
set
by
a
defining
property,
for
example
{
x
|
x
is
a
prime
number
less
than
10
}.
Sets
underpin
much
of
mathematics
and
logic,
and
form
the
foundation
of
axiomatic
set
theory,
such
as
Zermelo–Fraenkel
set
theory
(ZF)
and
ZFC
(ZF
with
the
Axiom
of
Choice).
to
illustrate
relationships
between
sets.
Mengde
provides
a
versatile
framework
for
describing
collections
of
objects
and
their
relationships
across
disciplines.