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przeliczalnego

Przeliczalnego is the genitive singular form of the Polish adjective przeliczalny, which in mathematical contexts is used to describe sets that are countable. The term przeliczalny refers to a property of being enumerable in a finite or countably infinite way, and it is contrasted with uncountable (nieprzeliczalny) in Polish mathematical literature.

In set theory, a set is przeliczalny (countable) if there exists a bijection between the set and

Key characteristics include that any subset of a przeliczalny zbiór is przeliczalny, and the union of a

Etymologically, przeliczalnego derives from przeliczyć (to count) with the suffix -alny, and the form shows grammatical

See also: przeliczalny zbiór, liczby przeliczalne, nieprzeliczalny.

the
natural
numbers.
This
includes
finite
sets
and
sets
that
are
in
bijection
with
N,
such
as
the
set
of
natural
numbers
themselves,
the
set
of
even
numbers,
the
set
of
integers,
and
the
set
of
rational
numbers.
By
definition,
the
real
numbers
are
not
przeliczalny;
they
form
an
uncountable
set.
finite
or
countable
family
of
przeliczalne
zbiory
(countable
sets)
is
itself
przeliczalny
under
standard
assumptions
in
set
theory.
These
concepts
are
central
to
cardinality
and
the
study
of
different
sizes
of
infinity.
inflection
appropriate
for
genitive
constructions
in
Polish
sentences,
such
as
“zbiór
przeliczalnego
typu”
or
similar
phrases.