Editing Intersection number (section)

== Applications ==

The intersection number is partly motivated by the desire to define intersection to satisfy [[Bézout's theorem]].

The intersection number arises in the study of [[fixed point (mathematics)|fixed point]]s, which can be cleverly defined as intersections of function [[graph of a function|graph]]s with a [[diagonal]]s. Calculating the intersection numbers at the fixed points counts the fixed points ''with multiplicity'', and leads to the [[Lefschetz fixed-point theorem]] in quantitative form.