Essays on the Theory of Numbers (Classic Reprint): I. Continuity and Irrational Numbers, II. The Nature and Meaning of Numbers: I. Continuity and ... and Meaning of Numbers (Classic Reprint) - Softcover

Inhaltsangabe

Discover how counting and arithmetic shape the real numbers and the foundations of analysis.

This edition presents Dedekind’s influential exploration of how the simplest act—counting—leads to the whole structure of rational and real numbers. It weaves together intuitive ideas with a rigorous arithmetic grounding, explaining what it means for numbers to be continuous and how irrational numbers arise from the limits of counting processes. The work frames a path from finite arithmetic to the infinite and complete real number system.

• How counting builds the infinite series of positive integers and underpins all of arithmetic
• The concept of completeness and the distinction between rational and real numbers
• Plain, step-by-step development of continuity and its role in analysis
• The idea of transforming and comparing number systems to understand infinity

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