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Foreword by Professor W H Cockcroft page
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addition and multiplication algebraic associative binary operation braids called cardinal number combination commutative complex numbers conjugate Consider the set continuous mapping coordinates curve defined definition denote diagram equation equivalence classes equivalence relation Example F Exercise factor group field finite follows form a group ft ft geometry given group G group of order group structure Hence homomorphic image idea identity element instance integers intersection introduced intuitive invariant subgroup inverse isometries isomorphic kernel label many-one mapping mathematics matrix multiplication modulo morphism multiplicative inverse natural numbers natural topology neutral element non-zero notation Note numbers under addition obtained one-one correspondence one-one mapping open set ordered pairs particular path permutations properties prove quaternion real numbers represented result rotation satisfies set of real solution subset topology symmetric symmetric difference theorem theory tion topological group topological space transformation translation triangle unique usual vector space zero