By Philip J. Davis, William G. Chinn (auth.)
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Extra resources for 3.1416 And All That
In the late nineteenth century, Giuseppe Peano of Italy provided a primitive description of the positive integers in terms of five axioms: (1) 1 is a positive integer; (2) every positive integer has a unique positive integer as its successor; (3) no positive integer has 1 as its successor; (4) distinct positive integers have distinct successors; (5) if a statement holds for the positive integer 1, and if, whenever it holds for a positive integer, it also holds for that integer's successor, then the statement holds for all positive integers.
1416 and All That and y may be, if the value of x agrees with the value of y, then y has this same value; so does xy. This can be stated: x + a +a = a and aa = a, and can be verified by inspecting the tables or by trying out all possible values for a( = 0, 1). The first is the property of simplicity for addition and the second the property of simplicity for multiplication. Another useful property to be noticed is that no matter what a is, a 1 = 1. This is a special case of the property called absorption.
Each of the three quantities, multiplied by itself, is equal to -1. \ -1 k -J . \ . -1 J J -k k k J . k . -\ 0 7 b. as a7 as 0 a7 6 8 a5 a4 5 -3 a2 I al 4 0 a5 a4 :""3 a2 3.