Editing Number sign (section)

=== Mathematics ===
* In [[set theory]], #''S'' is one possible notation for the [[cardinality]] or size of the [[set (mathematics)|set]] ''S'', instead of <math>|S|</math>. That is, for a set <math>S = \{s_1,s_2,s_3, \dots , s_n\}</math>, in which all <math>s_i</math> are mutually distinct, <math>\#S = n = |S|.</math> This notation is only sometimes used for [[finite set]]s, usually in [[number theory]], to avoid confusion with the [[divisibility]] symbol, e.g. <math>a \mid b</math>.
* In [[topology]], ''A''#''B'' is the [[connected sum]] of [[manifold]]s ''A'' and ''B'', or of knots ''A'' and ''B'' in [[knot theory]].
* In [[number theory]], ''n''# is the [[primorial]] of ''n''.
* In [[constructive mathematics]], # denotes an [[apartness relation]].
* In [[computational complexity theory]], [[♯P|#P]] denotes a [[complexity class]] of [[counting problem (complexity)|counting problems]]. The standard notation for this class uses the number sign symbol, not the [[sharp sign]] from music, but it is pronounced "sharp P". More generally, the number sign may be used to denote the class of counting problems associated with any class of search problems.