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Titlebook: Elementary Mathematics from a Higher Standpoint; Volume III: Precisio Felix Klein Book 2016 Springer-Verlag Berlin Heidelberg 2016 Geometry

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楼主: Guffaw
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II. Functions , (,) of a Real Variable ,he independent variable . can take on. We define that . must successively pass through the points of a certain “point set”. The language used is therefore geometric, but thanks to the Cantor-Dedekind Axiom (p. [7]) the arithmetical meaning is defined as well.
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Labeling Line Drawings of Polyhedra,t: If I use an empirical procedure such as drawing, measuring, evaluating by eye, or mental reproduction by spatial perception, the result of the construction only has limited accuracy; I will prove this for measuring, by showing some numerical values.
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Quantum Mechanics: Algebraic Point of Viewpirical space intuition; in this case one should not speak of lines and points, but always only of “stains” and stripes. The other possibility is to completely leave aside space intuition since it is misleading and to operate only with the abstract relations of pure analysis. .: In any case, I myself always advocated .
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V. Functions of Two Variableslations of approximation mathematics; on the other hand, this geometric representation allows us to refer to the ideal object and thus to indirectly clarify its meaning, like – for instance – we clarified the essence ofWeierstraß function by considering the successive approximating curves.
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Matrices with Polynomial Entries,the most basic definitions needed: .1. The coordinates ., . of a point are numbers according to the modern concept of number, that is, we define them as finite or infinite decimal fractions with a positive or negative sign. .2. A set of such points becomes, if it is infinite, object of a detailed mathematical analysis.
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