Index (n 1)-sphere, 133 2-sphere, 133 B3, 133 Bn, 133 S2, 133 Sn−1, 133 T0, 158 T1, 158 T2, 158 T3, 158 T4, 158 Q, 17 Qp, 179 Zn, 21 lim sup, 119 BC, 143 m × n matrix, 57 n-th root of unity, 114 p-adic absolute value, 176 p-adic completion of Q, 177 p-adic expansion, 181 p-adic field, 177 absolute value, 102 for C, 109 absolutely convergent series, 118 accumulation point, 104, 112, 132, 156 affine subspace, 69 algebra, 58 commutative, 58 with identity, 58 algebraic closure, 162 algebraic extension, 162 algebraic numbers, 115 algebraically closed, 114 angle between vectors, 71 Archimedean ordered field, 93 Archimedean property, 92 associative, 24 associativity of composition of functions, 24 automorphism of a field, 108 automorphism group of a field, 108 axiom, 43 axiom system, 43 base, 157 basis of a topological space, 157 vector space, 51 bijective, 24 bilinear form, 69 positive definite, 70 symmetric, 70 binary operations, 19 binomial coefficient, 15 Binomial Theorem, 15 Bolzano-Weierstrass, 139 Bolzano-Weierstrass Lemma, 103 Bolzano-Weierstrass Theorem, 104 boundary, 132 boundary point, 132 bounded, 90, 142 bounded above, 90 bounded below, 90 bounded sequence in C, 111 in Q, 99 in R, 103 189
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