A round-up on numbers

Part of the Universitext book series (UTX)
This chapter rounds up some basic notions about numbers; we shall need them later on, and it is useful to fix the ideas on some concepts and techniques which will be investigated in this book. Some of what follows will be studied again in more detail, but we shall assume a basic knowledge about:
  • some elements of set theory and logic (see for instance [43]);

  • the construction of the fundamental number sets:
    • ℕ = the set of natural numbers

    • ℤ = the set of integer numbers

    • ℚ = the set of rational numbers

    • ℝ = the set of real numbers,

    • ℂ = the set of complex numbers,

    and of the operations on them (see [15] or [22]);
  • the idea of limit and of numerical series (as given in any calculus text, for instance [12]);

  • some elements of algebra (see [4], [15], [32] or [45]): in particular, the reader will need the definitions of the main algebraic structures, like semigroups, groups, rings, integral domains, fields;

  • basic notions of linear algebra (see [13]): vector spaces, matrices, eigenvalues, and eigenvectors;

  • elementary concepts of probability theory (see [5] or [29]).


Rational Number Recurrence Relation Integral Domain Continue Fraction Great Common Divisor 
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© Springer-Verlag Berlin Heidelberg 2009

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