By James Fenimore Cooper
''A pleasant, funny, Swiftian satire, The Monikins tells of the mores of a society of polar monkeys in the course of the Gulliver-esque travels of Sir John Goldencalf, Esquire.''--P. [4] of cover.
summary: ''A pleasant, funny, Swiftian satire, The Monikins tells of the mores of a society of polar monkeys throughout the Gulliver-esque travels of Sir John Goldencalf, Esquire.''--P. [4] of canopy
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T H E BO O LE-SCH RÓ D ER ALG EBRA 37 This law obviously extends to sums of any number of terms, if a is a factor of each. It is an extremely important property of this algebra that if a given expression does not involve a particular term or element, there is always an equivalent expression which does. That is, we can always introduce any element we please into any given expression. The principle which makes this possible is called the Law of Expansion: 4*6 a = a (6 + -fc) = a 5 + a - 6 . [3-5] &+ - 6 = 1.
Hence a = a* 1 = a ( - a - 6) = (a -a ) -6 = 0 - - 6 = 0 . And 6 = 1-6 = ( - a - 6)6 = - a (-6 6) = - a -0 = 0. And if a = 0 and 6 = 0, a + 6 = 0 + 0 = 0 . In any algebra, if a = 0 and 6 = 0, then a + 6 = 0; but in this algebra the converse also holds: if a sum is null, each of its terms is null. Corresponding to the last two, by the Law of Duality, we have the two following: 4*8 4*81 If a 6 = x and a = 1, then 6 = x. a 6 = 1 is equivalent to the pair, a = 1 and 6 = 1. We turn now to the subject of equivalent equations of different forms: 4*9 a = 6 is equivalent to a - 6 + -a 6 = 0, and to a 6 + -a -6 = 1 .
And hence [ 1 - 02 ] a c 6 is equivalent to o + 6 = 6 . The next two theorems follow from previous principles by the Law of Transposition: 3*9 a c f l + 5 and b c a + b. [2 •4] -a -6 c -a and -a - 6 c -6. Hence [3 *81] a c - ( - a - 6) and b c - ( - a - 6). But [1 •03] - ( - a - 6) = a + 6 . 4- 2 acl. [2-6] 0 c - a . Hence [3*8] a c l . It is well to note that this obvious principle, “ Any class a is contained in the class of 1everything/ ” is equivalent to O c a , “ The null class is contained in every c l a s s a n d hence that the admission of either of these laws requires the other also.