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Senderos del Asombro

Caminos secundarios opcionales para los curiosos. Nunca cuentan en tu contra y siempre te devuelven a donde estabas.

Preescolar a 2.ºBoxes inside boxesWhat is inside a box that contains only an empty box? Is it empty? And can every description you can think of make a collection?Parte de Colecciones →SetsRussell's paradox and why sets need axiomsZFC: axiomatic set theorySeguir el sendero
6.º a 8.º gradoHow many infinities?There are infinitely many counting numbers and infinitely many infinite 0–1 sequences. Are these two infinities the same size?Parte de Sets →Countability and Cantor's diagonal argumentSeguir el sendero
6.º a 8.º gradoClock arithmeticIt's 9 o'clock. What time will it be in 5 hours — and in 29 hours? Can a clock teach us a whole new kind of arithmetic?Parte de Integers →Clock arithmetic: remainders and modular arithmeticCongruencesQuotient groups and quotient ringsSeguir el sendero
6.º a 8.º gradoInverses and structureEvery integer can be added to another integer to get $0$ . So why can almost no integer be multiplied by another integer to get $1$ ?Parte de Integers →Algebraic structures: monoids, groups and ringsGroupsRings, ideals and fieldsSeguir el sendero
6.º a 8.º gradoRemainder familiesSort every integer — positive, negative and zero — into families by its remainder after dividing by 3. If you add a member of one family to a member of another, does the family of the answer depend on which members you chose?Parte de Integers →Relations, equivalence relations and partitionsCongruencesQuotient groups and quotient ringsSeguir el sendero
9.º a 12.º gradoThe product, by its mapsCan you describe the set of pairs $A \times B$ without ever looking inside it — only by how functions go into it?Parte de Functions →Universal propertiesLimits and colimitsSeguir el sendero
9.º a 12.º gradoArrows that composeWhat do functions between sets, maps between groups and continuous maps between shapes have in common? What if we studied only the arrows?Parte de Composition →CategoriesFunctorsSeguir el sendero