G^N vs Set Theory Basics

G^N is a special calculator not just a game: This math app animates iterations of one or compositions of two multi-valued maps for free groups of in principle arbitrary finite rank in the abelian and non-commutative cases respectively (in this version the rank is restricted to values in between 2 and 11). Well-known examples of such multi-valued maps are permutations, for example the flip (x_1,x_2)->(x_2,x_1), in G^N we just write (1,2)->(2,1) and instead of the inverse we convenient flip the number. A more involved type of such a multi-valued map is the n+1 cycle defined by (1,...,n)->(-2-3-...-n-1,3,4,...,n,1), a non-trivial theorem. For example if n=2 this map is the hexagon (1,2)->(-2-1,1), this map applied twice reads (1,2)->(2,-2-1) and the third iteration is the identity map (1,2)->(1,2).

Set Theory Basics is an independent practice app for building confidence with core set theory ideas, notation, operations, relations, functions, proofs, and common reasoning traps. It is designed for students, self-learners, interview preparation, and anyone who wants focused review without account setup. Study across 160 questions organized by Fundamentals, Practical Skills, Common Pitfalls, and Advanced Concepts. Every question includes an explanation so you can learn from mistakes, not just count scores. - FSRS spaced-repetition intervals for smarter review - Weak-point heatmap to spot topics that need work - Daily challenge for consistent practice - Mock exams for timed review sessions - Offline practice with no login required - Clear explanations for every question Practice offline, no login required. Independent study app for Set Theory Basics practice. Not affiliated with, endorsed by, or sponsored by any company, certification body, exam operator, or vendor. All trademarks belong to their respective owners.