Quote: construct the real numbers as segments of series of rational ratios in order of magnitude; an irrational number is a segment without boundary

Quotation

We are now in a position to define a real number and an irrational number. An "real number" is a segment of the series of ratios in order of magnitude. An "irrational number" is a segment of the series of ratios which has no boundary. ... The real number 1, for instance, is the class of proper fractions. ... [p. 73] The above definition of real numbers is an example of "construction" as against "postulation"   Google-1   Google-2

Published before 1923

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