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siilii;: iliiiiil iiii i iijiii iiiiiif lii' ^iiiililiiiiii R.A FlY OE,F THE U N VERS ITY or IILLINOIS v.l _jjg,.^k*»t«r- Return this book on or before the Latest Date stamped below. EDUCATION. PHIIOSOPHY, PSYCHOLOGY LIBRARY University of Illinois Library ""^ I oTi^bb rBo4 ' JUN Q ''QQ.A X •p^^v'^' m -1964 T. LI61—H41 Digitized by the Internet Archive in 2011 with funding from University of Illinois Urbana-Champaign http://www.archive.org/details/highschoolmathemat01univ HIGH SCHOOL MATHEMATICS Unit 1. THE ARITHMETIC OF THE REAL NUMBERS UNIVERSITY OF ILLINOIS COMMITTEE ON SCHOOL MATHEMATICS ^ MAX BEBERAAAN, Direefor ^ HERBERT E. VAUGHAN, Editor 'O ^ II ^^ UNIVERSITY OF ILLINOIS PRESS • URBANA, 1959 -0 ^> C 1959 by lh« Board of Truiteei of the Univeriity of Illinois. AAonufoclured in the United Slates of America. f Instructions for integrating the green pages with the white pages COMMENTARY The green sheets of the occur in blocks [each consist- ing of one or naore sheets] each of which contains discussions referring to a single page or a group of consecutive pages of the text (white sheets). The pages of the text to which a block of green sheets refers are listed in brackets at the foot of each sheet. Thus, 'TC[l-A, B, C]* indicates that this sheet refers to pages 1 -A, 1-B, and 1-C. And, 'TC[l-J]a', 'TC[l-J]b', and 'TC[l-J]c' indicate members of a block of green sheets all of which refer to page 1-J. Each block should be inserted among the pages of the text so that the printed side of its first sheet faces the first text page to which it refers. For example, the sheet labeled 'TC[l-A, B, C]' should face page 1 -A of the text. And, the sheet labeled 'TC[l-J]a' should face page 1-J of the text, and be backed up by the sheets labeled 'TC[l-j]b' and 'TC[l-J]c'. The final result should be that, on turning to a page of the text, one has opposite it the first of the green pages [if any] which refer to it. And, if there are several such pages, one obtains a view of the second by turning the first, etc. An exception to these instructions is that the introductory green pages of each unit are to follow the title page of that unit. For your convenience, we list the first several pages of the completely integrated Teachers' Edition. Title page, blank], [l/l, blank], [l/2, blank], [l/3, blank], 'l/A, blanlc], [1/5, blanlc], [i, ii], [iii, iv], [blank, l/6], l-A, 1-B], [1-C, 1-D], [1/7, blank], [l-E, 1-F], [1-G, 1-H], l-I, 1-J], [1/8, blank], [l/9, blank], [l/lO, blank], [blank, l/l 2], blank, l/l 1], [1-K, l-L], [l/l 3, blank], [l/l4, blank], blank, l/i7], [blank, 1/16], [blank, l/l5], [1-M, 1-N], 1/18, blank], [blank, l/20], [blank, l/l9], [l-O, blank], "blank, l/22], [blank, l/21],[l-l, 1-2], [l/23, blank], ;i-3, 1-4], [1/24, blank], [blank, l/25], ... Note The numerals 'l/l\ 'l/2', ... are useful for assembling the : green pages in order for those who do not want to integrate them with the white pages.