The Fundamental Laws of Addition And Multiplication in Elementary Algebra
The Fundamental Laws of Addition And Multiplication in Elementary Algebra
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O © 5= 6 © «. ] *See fi. Borel and J. Drach, Theorie des nombres et Valyebre supMeure, 1896, p. 157. Fof t, n early statement of the problem, compare H. Hankel, loc. Cit. , 1867, §12.
1906] FUNDAMENTAL LAWS OF AUDITION AND MULTIPLICATION 33 Ml. A Q b in the system.
M2. (a Q b) o c = a Q (b Q c).
MS, (I) liaQx = aQy and a ® a :^ a, then x = y.
(2) \ixQa — yQa and a ® a ^ a, then a; = y. IT/4. (1) a o (6 ® c) = (a o 6) e (a o c).
(2) (6 e c) a = (6 a) ® (c a). J/5. A Q h — b Q a.
Examples of pseu...do-algebras.
The examples which prove the independence of the several postulates are the following, all of which are constructed out of numerical classes with which the reader has already been made familiar in §3.
All except A\. The class of all rational numbers, with ® and o defined as follows : a ® b — a -\- b whenever a -\- b — Q ; otherwise, a ® b not in the class, a 6 = ab, where ab denotes the ordinary product.
All except A2. The class of all rational numbers, a e 6 = 2(a + i).
What to read after The Fundamental Laws of Addition And Multiplication in Elementary Algebra?
You can find similar books in the "Read Also" column, or choose other free books by E V Edward Vermilye Huntington to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
O © 5= 6 © «. ] *See fi. Borel and J. Drach, Theorie des nombres et Valyebre supMeure, 1896, p. 157. Fof t, n early statement of the problem, compare H. Hankel, loc. Cit. , 1867, §12.
1906] FUNDAMENTAL LAWS OF AUDITION AND MULTIPLICATION 33 Ml. A Q b in the system.
M2. (a Q b) o c = a Q (b Q c).
MS, (I) liaQx = aQy and a ® a :^ a, then x = y.
(2) \ixQa — yQa and a ® a ^ a, then a; = y. IT/4. (1) a o (6 ® c) = (a o 6) e (a o c).
(2) (6 e c) a = (6 a) ® (c a). J/5. A Q h — b Q a.
Examples of pseu...do-algebras.
The examples which prove the independence of the several postulates are the following, all of which are constructed out of numerical classes with which the reader has already been made familiar in §3.
All except A\. The class of all rational numbers, with ® and o defined as follows : a ® b — a -\- b whenever a -\- b — Q ; otherwise, a ® b not in the class, a 6 = ab, where ab denotes the ordinary product.
All except A2. The class of all rational numbers, a e 6 = 2(a + i).
What to read after The Fundamental Laws of Addition And Multiplication in Elementary Algebra?
You can find similar books in the "Read Also" column, or choose other free books by E V Edward Vermilye Huntington to read onlineMoreLess
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