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By Charlotte Baker-Shenk, Dennis Cokely

Cokely D., Baker-Shenk C. American signal Language.. A pupil textual content, devices 1-9 (Gallaudet college Press, 1991)(ISBN 0930323866)(400dpi)(194s)

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Sample text

Always possible. 2. Unique. 3. Associative law. 4. Commutative law. 5. Monotonic law. Notice, in connection with 5, that a < b means, now, that a lies to the left of b in the geometric representation, so that we have, for example 2 < 1, 3 < C2. 1. Negative Numbers 27 The chief point in the multiplication of positive and negative numbers is the rule of signs, that a . c/ D . a c/, and . c/. c c 0 /. Especially the latter rule: “Minus times minus gives plus” is often a dangerous stumbling block. We shall return presently to the conceptual significance of these rules; just now we shall combine them into a statement defining multiplication of a series of positive and negative numbers: The absolute value of a product is equal to the product of the absolute values of the factors; its sign is positive or negative according as an even or an odd number of factors is negative.

Whereas, before, the possibility of logical operation began only after the eleven fundamental laws had been set up, it can start earlier here, after the simpler ones 3. The Logical Foundations of Operations with Integers 15 have been selected. The boundary between intuition and logic is displaced in favour of the latter. Hermann Graßmann did pioneer work in this direction in his Lehrbuch der Arithmetik17 in 1861. As an example from it, I mention merely that the commutative law can be derived from the associative law by the aid of the principle of mathematical induction.

It seems to me that one must retain a remainder, albeit a minimum, of intuition. One must always tie a certain intuition, even in the most abstract formulation, with the symbols one uses in operations, in order to be able always to recognise the symbols again, even if one thinks only about the shape of the letters. c) Let us even assume that the proposed problem has been solved in a way free from objection, that the compatibility of the eleven fundamental laws has been On the foundations of logic and arithmetic.

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