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Equinumerosity is
compatible with the
basic set
operations in a way that
allows the
definition of
cardinal arithmetic. Specifically,
equinumerosity is...
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under the
equivalence relation of
equinumerosity. This
definition may
appear circular, but it is not,
because equinumerosity can be
defined in
alternate ways...
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defined as follows. The
relation of
having the same
cardinality is
called equinumerosity, and this is an
equivalence relation on the
class of all sets. The equivalence...
- theory, this is
taken as the
definition of "same
number of elements" (
equinumerosity), and
generalising this
definition to
infinite sets
leads to the concept...
-
classes on the
entire universe of sets, by
equinumerosity). The
concepts are
developed by
defining equinumerosity in
terms of
functions and the
concepts of...
-
cardinality is
sometimes referred to as equipotence, equipollence, or
equinumerosity. It is thus said that two sets with the same
cardinality are, respectively...
- "propositional function", and in particular,
relations of "similarity" ("
equinumerosity":
placing the
elements of
collections in one-to-one correspondence)...
- of
Equivalence relations:
Equality Parallel with (for
affine spaces)
Equinumerosity or "is in
bijection with"
Isomorphic Equipollent line
segments Tolerance...
-
cardinal number is an
equivalence class of sets
under the
relation of
equinumerosity: the sets A and B are
equinumerous if
there exists a
bijection between...
-
denotes the
power class of x and “≈{\displaystyle \approx }”
denotes equinumerosity. What Tarski's
axiom states (in the vernacular) is that for each set...
