## Problems for mathematicians, young and old |

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abelian group additive group algebra answer is yes automorphism calculus Cantor function Cantor set Cesaro continuous Chapter checkerboard chord circles closed intervals colors commute complement Conclusion congruent Consequence consider convergent convex set countable set decreasing sequence defined diagonal disjoint union dominoes elements equal equation exactly example exist extreme points FIGURE fixed point follows happens homeomorphic implies induction infinite instance intersection inverse isomorphic Lebesgue measure linear transformation look magic square mathematical matrix modulo monic polynomials monotone subsequences multiples non-empty open intervals plane polynomial positive integers positive measure positive number possible probability proof question rational numbers real numbers rectangle result second player segment semigroup sequence of length square root square-free subsequences of length subset subspaces theorem tiled tion topological topological groups toss triangle trivial true uncountable unit interval vector space words zero