Definition·D064
Embedding of the integers into the rationals
Each integer n corresponds to the rational represented by the pair (n, 1).
for
, with
the rationals and
(D057).
In words
The embedding sends an integer n to the class of the pair (n, 1): the rational that is n over one.
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 L56. Composed with ι,
embeds the naturals into the rationals as well. Write
for
and
for
in
.