Revision as of 07:00, 27 July 2025 edit David Eppstein (talk \| contribs) Autopatrolled, Administrators 235,852 edits This was CS1 in 2016; standardize on that. Supply requested citation. ← Previous edit		Revision as of 07:05, 27 July 2025 edit undo David Eppstein (talk \| contribs) Autopatrolled, Administrators 235,852 edits →Properties: spell out that this provides a dense set of local maxima (as a sequence of papers in the Monthly in the mid-1980s repeatedly studied this topic and failed to note this simple example) Next edit →
Line 84: {{Collapse bottom}} \|<math>f</math> has a ~~strict~~proper '''[[maxima and minima\|local maximum]]''' at each rational number, providing an example of a function with a dense set of local maxima.<ref>{{cite journal\|title=Solution to Problem 1129\|first=Paolo\|last=Perfetti\|department=Problem Department\|journal=Pi Mu Epsilon Journal\|volume=12\|issue=5\|date=Fall 2006\|pages=301–319\|jstor=24337958}} Perfetti supplies the negation of Thomae's function as an example with a dense set of proper local minima.</ref> {{pb}} See the proofs for continuity and discontinuity above for the construction of appropriate [[neighborhood (mathematics)\|neighbourhoods]], {{nowrap\|where <math>f</math> has}} maxima.

Thomae's function: Difference between revisions