Definition·D060
Multiplication of integers
Multiply integers by the cross formula on representative pairs, mirroring how (a minus b) times (c minus d) expands.
For
, write
and
with
, and define
(using natural-number addition and multiplication). This does not depend on the choice of representatives, so
is a well-defined binary operation on
.
In words
To multiply two integers, pick representative pairs and cross-multiply and add according to the rule for (a minus b) times (c minus d), taking the class of the result.
Rests onA02
Never needed: F02 · F03 · F04 · F05 · F06 · F08 · F09 · F10 · F11 · F12 · F13 · F14 · A01 · A03 · A04 · A05 · A06 · A07 · A08 (computed from the citation graph, not asserted).