A Formal Framework And Fundamental Results for Social Analysis
A Formal Framework And Fundamental Results for Social Analysis
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COR . Any (collective) reaction is non-empty.
Proof : Let p be any social state, let q-^ = I (p (p)), and let the subset Q of P be defined by Q = {q| q = q. * qj}, (q. M P _. ) .
Q is bounded, since P is bounded. Since P. Is closed, so is Q closed. Thus, Q is compact. Hence, the continuous (real-valued) function U, attains a maximum on Q. Thus, Y (p) = {rl U(r) - Max U(q) } 5« (2, (j in N), J qeQ Y„(p) i 0, by definition. Hence, also Y(p) i 0, 12 14. DEF . Let Y(p) be the collective reaction of... N to the social state p, and let y = (r-, ... , r ) denote the generic element of Y(p) . A social state z such that (Po(^)> •••. Pn(z)) = y Is called an elementary manifestation of y, and the Z(y) of all such is called the manifestation of y. The set Z(Y(p)), Z(Y(p)) = M Z(y) yeY(p) of all elementary manifestations of elementary collective reactions y in Y(p) is called the manifestation of Y(p) .
15. DEF. A correspondence S, p S: P > 2, such that S(p) = Z(Y(p)), is called a social evolution .
What to read after A Formal Framework And Fundamental Results for Social Analysis?
You can find similar books in the "Read Also" column, or choose other free books by Murat R Sertel to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
COR . Any (collective) reaction is non-empty.
Proof : Let p be any social state, let q-^ = I (p (p)), and let the subset Q of P be defined by Q = {q| q = q. * qj}, (q. M P _. ) .
Q is bounded, since P is bounded. Since P. Is closed, so is Q closed. Thus, Q is compact. Hence, the continuous (real-valued) function U, attains a maximum on Q. Thus, Y (p) = {rl U(r) - Max U(q) } 5« (2, (j in N), J qeQ Y„(p) i 0, by definition. Hence, also Y(p) i 0, 12 14. DEF . Let Y(p) be the collective reaction of... N to the social state p, and let y = (r-, ... , r ) denote the generic element of Y(p) . A social state z such that (Po(^)> •••. Pn(z)) = y Is called an elementary manifestation of y, and the Z(y) of all such is called the manifestation of y. The set Z(Y(p)), Z(Y(p)) = M Z(y) yeY(p) of all elementary manifestations of elementary collective reactions y in Y(p) is called the manifestation of Y(p) .
15. DEF. A correspondence S, p S: P > 2, such that S(p) = Z(Y(p)), is called a social evolution .
What to read after A Formal Framework And Fundamental Results for Social Analysis?
You can find similar books in the "Read Also" column, or choose other free books by Murat R Sertel to read onlineMoreLess
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