Editing Empty set (section)

=== Operations on the empty set ===

When speaking of the [[summation|sum]] of the elements of a finite set, one is inevitably led to the convention that the sum of the elements of the empty set (the [[empty sum]]) is zero. The reason for this is that zero is the [[identity element]] for addition. Similarly, the [[multiplication|product]] of the elements of the empty set (the [[empty product]]) should be considered to be [[1 (number)|one]], since one is the identity element for multiplication.<ref>{{cite book |author=David M. Bloom |title=Linear Algebra and Geometry |url=https://archive.org/details/linearalgebrageo0000bloo |url-access=registration |year=1979 |isbn=0521293243 |pages=[https://archive.org/details/linearalgebrageo0000bloo/page/45 45]}}</ref>

A [[derangement]] is a [[permutation]] of a set without [[fixed point (mathematics)|fixed point]]s. The empty set can be considered a derangement of itself, because it has only one permutation (<math>0!=1</math>), and it is vacuously true that no element (of the empty set) can be found that retains its original position.