Displaying similar documents to “On the Arithmetic of Errors”

A Mathematical Basis for an Interval Arithmetic Standard

Bohlender, Gerd, Kulisch, Ulrich (2010)

Serdica Journal of Computing

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Basic concepts for an interval arithmetic standard are discussed in the paper. Interval arithmetic deals with closed and connected sets of real numbers. Unlike floating-point arithmetic it is free of exceptions. A complete set of formulas to approximate real interval arithmetic on the computer is displayed in section 3 of the paper. The essential comparison relations and lattice operations are discussed in section 6. Evaluation of functions for interval arguments is studied in section...

Solving a ± b = 2c in elements of finite sets

Vsevolod F. Lev, Rom Pinchasi (2014)

Acta Arithmetica

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We show that if A and B are finite sets of real numbers, then the number of triples (a,b,c) ∈ A × B × (A ∪ B) with a + b = 2c is at most (0.15+o(1))(|A|+|B|)² as |A| + |B| → ∞. As a corollary, if A is antisymmetric (that is, A ∩ (-A) = ∅), then there are at most (0.3+o(1))|A|² triples (a,b,c) with a,b,c ∈ A and a - b = 2c. In the general case where A is not necessarily antisymmetric, we show that the number of triples (a,b,c) with a,b,c ∈ A and a - b = 2c is at most (0.5+o(1))|A|². These...

Textes & documents - A new source for medieval mathematics in the iberian peninsula: the commercial arithmetic in Ms 10106 (Biblioteca Nacional, Madrid)

Javier Docampo Rey (2009)

Revue d'histoire des mathématiques

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This paper contains a critical edition of a short commercial arithmetic written in Castilian (ca. 1400). The manuscript has certain characteristic features, like the presence of composite fractions, that distinguishes it from other known treatises of the Iberian peninsula. The document appears to improve considerably our knowledge of the origins and the transmission of vernacular commercial arithmetic in Europe.