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| Based on the integer system, the real number system, and the axioms of structure, we establish the discrete real number system and the new calculus theory. These works constitute the foundation of the new mathematics which possesses the properties of scale, quantization, uncertainty and finite precision. The new mathematics, with a structure constant C, does not include the concepts of limit, infinity and infinitesimal, however, it can degenerate into the existing mathematics in the case of limit C→∞ . |
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| Keywords:basic mathematics; disrete real number; calculus |
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