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01valued

01valued, often written as 0-1 valued, is a term used to describe mathematical objects, functions, or data that take only the two values 0 and 1. In mathematics, a 01-valued function is a mapping f from a set X to the set {0,1}. Such functions are commonly called indicator or characteristic functions, as they indicate membership of elements in a subset A of X: f(x) equals 1 if x is in A and 0 otherwise.

In probability and statistics, a 01-valued variable is known as a binary or indicator random variable. It

Key properties of 01-valued objects include their restricted range to {0,1}. Logical operations align with arithmetic:

See also indicator function, Boolean algebra, binary variable, and 0-1 encoding for related concepts.

represents
the
occurrence
or
non-occurrence
of
an
event,
with
expectations
matching
the
event’s
probability.
In
graph
theory,
adjacency
matrices
of
simple
graphs
are
typically
01-valued,
containing
1s
where
vertices
are
connected
and
0s
otherwise.
In
computer
science,
01-valued
data
underpins
boolean
logic,
binary
encoding,
and
digital
signals,
where
0
and
1
denote
false
and
true
or
off
and
on,
respectively.
AND
corresponds
to
minimum,
OR
to
maximum
(under
standard
0/1
interpretation),
and
complement
to
1
minus
the
value.
This
allows
boolean
expressions
to
be
translated
into,
and
manipulated
as,
arithmetic
expressions
using
0
and
1.