The Arithmetic of Algebraic Numbers: An Elementary Approach
نویسندگان
چکیده
منابع مشابه
The Arithmetic of Algebraic Numbers: An Elementary Approach
Let Q and R be the fields of rational and real numbers respectively. Recall that a real number r is algebraic over the rationals if there is a polynomial p with coefficients in Q that has r as a root, i.e., that has p(r) = 0. Any college freshman can understand that idea, but things get more challenging when one asks about arithmetic with algebraic numbers. For example, being the roots of x2− 3...
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Elementary arithmetic
There is a quite natural way in which the safe/normal variable discipline of Bellantoni-Cook recursion (1992) can be imposed on arithmetical theories like PA: quantify over safes and induct on normals. This weakens the theory severely, so that the provably recursive functions become more realistically computable (slow growing rather than fast growing). Earlier results of Leivant (1995) are re-w...
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ژورنال
عنوان ژورنال: The College Mathematics Journal
سال: 2004
ISSN: 0746-8342
DOI: 10.2307/4146920