Quote: solve algebraic equations by generalization of addition by iteration: get negative numbers and reciprocal powers from subtraction, fractions from division, irrationals from fractional powers, and complex numbers from the square root of -1

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If we start with a certain number a, … call a+b, and that defines addition of integers. … [p. 22-2] Now here is the idea. These relationships … [such as a(b+c)=ab+ac] … raising to a power. We are going to … represent so that they will obey these same … [p. 22-3] Thus, rather than using integers symbolically to … a more general kind of number. [from subtraction get negative numbers, from subtraction of powers get reciprocal powers, from division get fractions, from fractional powers get irrational numbers, complex by square root of negative numbers] … [p. 22- 8] But it turns out that with this …   Google-1   Google-2

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Related Topics

Group: philosophy of mathematics   (11 topics, 330 quotes)
Topic: kinds of numbers (24 items)