Sentence Examples


  • Peirce, "Mathematics is the science which draws necessary conclusions" (Linear Associative Algebra, § i.
  • The latter is the more advanced process, implying some knowledge of the laws of fractional numbers, as well as an application of the associative law (� 26 (i.)).
  • (a) The commutative law and the associative law are closely related, and it is best to establish each law for the case of two numbers before proceeding to the general case.
  • Thus a(b+c) and (b+c)a give the same result, though it may be written in various ways, such as abdac, ca+ab, &c. In the same way the associative law is that A(BC) and (AB)C give the same formal result.
  • They are (a+b)-?-c=a+(b+c) (A) (aXb)Xc=aX(bXc) (A') a+b=b+a (c) aXb=bXa (c') a(b c) =ab-Fac (D) (a - b)+b=a (I) (a=b)Xb=a (I') These formulae express the associative and commutative laws of the operations + and X, the distributive law of X, and the definitions of the inverse symbols - and =, which are assumed to be unambiguous.

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