By Buaer P.S.
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Extra resources for Dissipative Dynamical Systems I
Example text
Between any two supposedly adjacent atomic numbers, chemists have repeatedly found a third. Then if there are less than one hundred elements and we cannot necessarily infer the falsity of 1. 2 is true, Principle 2a and its generalizations are very important, as the sequel will show, and for the sake of convenience we give them a name, the Law of Contradiction and Interchange. " This principle, under a different form, plays a very important role, especially in mathematics. " This consists simply in assuming that the theorem to be proven is false, and then demonstrating that an inconsistency with certain assumptions occurs.
Before investigating the laws of this science, a few preliminary definitions and remarks are necessary. " This term is really fundamental and no precise definition can be given. But we may distinguish the term "proposition" from other allied expressions by recalling the distinction made in elementary grammar between declarative sentences and 17 . ELEMENTS OF LOGIC 18 Other types of sentences, for a proposition is essentially the former. " are not propositions in our sense of the word. But the logician makes a distinction between two different compare these declarative types of propositions.
We — — resent this specific value by the letter a; hy X — y. , equal to + 1 + x"); — x'y x" — y" is divisible . ELEMENTS OF LOGIC 32 we have merely added and latter may be written since subtracted the same quantity, xy. The x"*^ x''(x But this last expression — xy xy — y" + s — y) + y (x" — y"). -{- is divisible obviously is, and the latter part is the last expression is equal to x"''^ or — by x y, since the first part by hypothesis. Hence, since — y"''^, we may say that this — y. " But, as a matter of fact, x^ — y, or X — y, divisible by x — y.
Dissipative Dynamical Systems I by Buaer P.S.
by Thomas
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