Transitivity (Mathematics)
In
mathematics
, the word
transitive
admits at least two distinct meanings:
A
group
G
acts
transitively
on a
set
S
if for any
x
,
y
∈
S
, there is some
g
∈
G
such that
gx
=
y
. See
group action
. A somewhat related meaning is explained at
ergodic theory
.
A
binary relation
is
transitive
if whenever A is related to B and B is related to C, then A is related to C, for all A, B, and C in the domain of the relation. See
transitive relation
.
See also
transitive closure
,
intransitivity
.
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