Definition·D057
Embedding of the naturals into the integers
Each natural number n corresponds to the integer represented by the pair (n, 0).
for
(D026), with
the integers.
In words
The embedding sends a natural number n to the class of the pair (n, 0): the integer that is n minus zero.
Rests onno axioms yet
Never needed: F02 · F03 · F04 · F05 · F06 · F08 · F09 · F10 · F11 · F12 · F13 · F14 · A01 · A02 · A03 · A04 · A05 · A06 · A07 · A08 (computed from the citation graph, not asserted).
Remarks
Exists as a function by Separation, carved out of
as
. Injectivity is L42; compatibility with
and
is L46, and with the order L49. Write
for
and
for
; through this embedding every natural number is identified with an integer, and
is regarded as extending
.