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By Peter Calingaert

Assemblers, compilers, and application translation (Computer software program engineering sequence)

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How shall we decide whether two collections are to belong to the same bundle? ” But this presupposes that we have defined numbers, and that we know how to discover how many terms a collection has. We are so used to the operation of counting that such a presupposition might easily pass unnoticed. In fact, however, counting, though familiar, is logically a very complex operation; moreover it is only available, as a means of discovering how many terms a collection has, when the collection is finite.

In all these cases, when the relation holds between x and y, it also holds between y and x. But with serial relations such a thing cannot happen. A relation having this first property is called asymmetrical. (2) If x precedes y and y precedes z, x must precede z. This may be illustrated by the same instances as before: less, earlier, left of. But as instances of relations which do not have this property only two of our previous three instances will serve. If x is brother or sister of y, and y of z, x may not be brother or sister of z, since x and z may be the same person.

In seeking a definition of number, the first thing to be clear about is what we may call the grammar of our inquiry. Many philosophers, when attempting to define number, are really setting to work to define plurality, which is quite a different thing. Number is what is characteristic of numbers, as man is what is characteristic of men. A plurality is not an instance of number, but of some particular number. A trio of men, for example, is an instance of the number 3, and the number 3 is an instance of number; but the trio is not an instance of number.

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