- 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...
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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...
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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...
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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...
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whole set of real numbers. In
other words, the open
interval (a,b) is
equinumerous with R {\displaystyle \mathbb {R} } , as well as with
several other infinite...
- of its
power set is a Dedekind-infinite set,
having a
proper subset equinumerous to itself. If the
axiom of
choice is also true, then
infinite sets are...
- the same
cardinality are, respectively, equipotent, equipollent, or
equinumerous. Formally, ****uming the
axiom of choice, the
cardinality of a set X is...
-
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)...
