اختياري · لا يُقيَّم أبدًا
مسارات الدهشة
مسارات جانبية اختيارية لمحبّي الاستطلاع. لا تُحسب ضدك أبدًا، وتعيدك دائمًا إلى حيث كنت.
- الروضة–الصف الثانيBoxes 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?ينطلق من التجمّعات →SetsRussell's paradox and why sets need axiomsZFC: axiomatic set theoryاتبع المسار
- الصفوف 6–8How many infinities?There are infinitely many counting numbers and infinitely many infinite 0–1 sequences. Are these two infinities the same size?ينطلق من Sets →Countability and Cantor's diagonal argumentاتبع المسار
- الصفوف 6–8Clock 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?ينطلق من Integers →Clock arithmetic: remainders and modular arithmeticCongruencesQuotient groups and quotient ringsاتبع المسار
- الصفوف 6–8Inverses and structureEvery integer can be added to another integer to get . So why can almost no integer be multiplied by another integer to get ?ينطلق من Integers →Algebraic structures: monoids, groups and ringsGroupsRings, ideals and fieldsاتبع المسار
- الصفوف 6–8Remainder 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?ينطلق من Integers →Relations, equivalence relations and partitionsCongruencesQuotient groups and quotient ringsاتبع المسار
- الصفوف 9–12The product, by its mapsCan you describe the set of pairs without ever looking inside it — only by how functions go into it?ينطلق من Functions →Universal propertiesLimits and colimitsاتبع المسار
- الصفوف 9–12Arrows that composeWhat do functions between sets, maps between groups and continuous maps between shapes have in common? What if we studied only the arrows?ينطلق من Composition →CategoriesFunctorsاتبع المسار