From Counting to Continuum

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This introduction to real numbers offers a clear, step-by-step exploration of mathematical concepts, starting from the intuitive idea of counting. It gradually builds on simpler number types, defining each in relation to the previous one through equivalence relations. Natural numbers emerge from finite sets, integers from pairs of natural numbers, and modular numbers from integers, creating a coherent framework. The book is designed for newcomers to university-level mathematics, featuring exercises and solutions to reinforce understanding.