- In mathematics, two sets or
classes A and B are
equinumerous if
there exists a one-to-one
correspondence (or bijection)
between them, that is, if there...
-
German mathematician Richard Dedekind) if some
proper subset B of A is
equinumerous to A. Explicitly, this
means that
there exists a
bijective function from...
-
defined in
alternate ways, for
instance by
saying that two sets are
equinumerous if they can be put into one-to-one correspondence—this is
sometimes known...
-
where A and B are
equinumerous with a
subset of the
other set—that is, A is
equinumerous with a
subset of B and B is
equinumerous with a
subset of A...
- the same
cardinality are, respectively, equipotent, equipollent, or
equinumerous. Formally, ****uming the
axiom of choice, the
cardinality of a set X is...
-
theorem that A = c B {\displaystyle A=_{c}B} i.e. A and B are
equinumerous, but they do not have to be
literally equal (see isomorphism). That at...
-
these is its
initial ordinal. Any set
whose cardinality is an
aleph is
equinumerous with an
ordinal and is thus well-orderable. Each
finite set is well-orderable...
-
axiom of choice),
provided that the ur-elements form a set
which is
equinumerous with a pure set (a set
whose transitive closure contains no ur-elements)...
- Previously, all
infinite collections had been
implicitly ****umed to be
equinumerous (that is, of "the same size" or
having the same
number of elements)....
- is not a set. Two
classes are
equinumerous iff a
bijection exists between them. A
class is
infinite iff it is
equinumerous with one of its
proper subclasses...
