Monthly Archives: December 2013

A mathematical view on the notion of “median”

These days we hear about medians of all kinds of things: household income, lifetime of items such as lightbulbs, and so on. It’s time to get a rigorous grip on the concept. Definition. Suppose is a set, a totally ordered … Continue reading

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Adventskranz-Rätsel

Beim Anzünden der Kerzen unseres Adventskranzes heute morgen hat es mich gestört, keinen guten Algorithmus zu haben, dass die Kerzen möglichst gleichmässig “belastet” werden. Das hat mich zu folgendem vereinfachten Rätsel inspiriert: In Adventswoche (für ) werden Kerzen gewählt, angezündet, … Continue reading

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Math facts with simple proofs that are still (somewhat) surprising

Sometimes it happens to me that I become aware of a mathematical fact that surprises me – and the proof for the fact would even fit in a tweet. When goofing around with graph homomorphisms, I realised that the following … Continue reading

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Sometimes a maximality principle is true even if Zorn’s Lemma fails

A famous and straightforward result in general topology says that any compact space is maximally compact: any finer topology isn’t compact any more; minimally : any coarser topoology isn’t any more. A natural pair of questions that arises from this … Continue reading

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On empty Hom-sets between graphs

In many categories such as Set, Group, Top (topological spaces) there is a morphism between any two objects, usually in both directions. (If one object is “empty”, like the empty space, or the empty set, there is the “empty” morphism … Continue reading

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On the topological closure of the diagonal of a space

When we take a class in general topology and learn about -spaces, one of the standard exercises we do is: Prove that a space is Hausdorff if and only if the diagonal is closed in the product topology of . … Continue reading

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