Numbers and Infinity: A Historical Account of Mathematical Concepts
Perfect for either undergraduate mathematics or science history courses, this account presents a fresh and detailed reconstruction of the development of two mathematical fundamentals: numbers and infinity. One of the rare texts that offers a friendly and conversational tone, it avoids tedium and controversy while maintaining historical accuracy in defining its concepts' profound mathematical significance.
The authors begin by discussing the representation of numbers, integers and types of numbers, and cubic equations. Additional topics include complex numbers, quaternions, and vectors; Greek notions of infinity; the 17th-century development of the calculus; the concept of functions; and transfinite numbers. The text concludes with an appendix on essay topics, a bibliography, and an index.
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algebraic equations algebraic numbers analysis angle Archimedes argument arithmetic calculus Cantor Cardan’s cardinal number Chapter circle complex numbers computers concept construct continuous functions continuum hypothesis cube cubic equation curve decimal representation deﬁned deﬁnite integral deﬁnition denumerable developed differential dimensions discovery equal Euclid Euler example factorisation Fermat ﬁeld ﬁgure ﬁnally ﬁnd ﬁnding ﬁrst formula Fourier Fourier series fractions function fundamental generalisation geometrical give given Greek hypercomplex idea indeﬁnite inﬁnite sets inﬁnitely small inﬁnitesimal integers irrational numbers Leibniz linear logarithms mathematicians mathematics matrices method method of exhaustion modern multiplication natural numbers Newton non-Euclidean geometry notion nowadays number system obtain polygon positive integers prime numbers problem proof properties quadratic equations quantum quaternions question rational numbers real numbers realised rectangles result roots rotation rules satisﬁes sexagesimal signiﬁcance simple solution space square tangent theorem theory tions transﬁnite triangles unit fractions vector whole numbers zero