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Naturales

Naturales, or natural numbers, are the set of numbers used for counting and basic ordering. In mathematics they are usually denoted by N. Depending on the convention, N either includes zero (0, 1, 2, 3, …) or starts at one (1, 2, 3, …).

Historically, their formal foundation is provided by axioms such as the Peano axioms. These specify a distinguished

Natural numbers are closed under addition and multiplication, forming a primitive algebraic structure. They are naturally

Key concepts include the successor function, addition and multiplication as recursive operations, and the principle of

Variants: Some authors include zero as a natural number; others do not. In some contexts the term

element
(often
0)
and
a
successor
function
S,
where
every
number
has
a
unique
successor,
and
0
is
not
the
successor
of
any
number.
The
induction
axiom
allows
proofs
by
induction
over
natural
numbers.
ordered,
with
the
usual
less-than
relation,
and
the
order
is
compatible
with
addition
and
multiplication.
The
set
of
natural
numbers
is
infinite
and
serves
as
the
basis
for
arithmetic.
mathematical
induction.
Natural
numbers
underpin
many
branches
of
mathematics,
including
number
theory,
combinatorics,
and
set
theory,
and
they
serve
as
the
counting
basis
in
everyday
life
and
computer
science.
'whole
numbers'
is
used
to
denote
nonnegative
integers
(including
zero).