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Tri-Operational Algebra

In: Selecta Mathematica

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  • Karl Menger

Abstract

In classical analysis we start with a field of numbers. A function is explicitly defined as a set of pairs of numbers (x, f (x)) in which x ranges over what is called the domain of f. Also equality, addition, multiplication, and substitution of functions are explicitly defined. The structure of classical analysis is somewhat comparable to that of classical projective geometry. Veblen and Young start with a set whose elements are called points, and then explicitly define lines and planes as certain sets of points. Also joining and intersecting are introduced in set-theoretical terms.

Suggested Citation

  • Karl Menger, 2003. "Tri-Operational Algebra," Springer Books, in: Bert Schweizer & Abe Sklar & Karl Sigmund & Peter Gruber & Edmund Hlawka & Ludwig Reich & Leopold Sc (ed.), Selecta Mathematica, pages 181-188, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-6045-9_20
    DOI: 10.1007/978-3-7091-6045-9_20
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