Download My Book Of Number Games 1-70 (Kumon Workbooks) by Shinobu Akaishi, Eno Sarris PDF

By Shinobu Akaishi, Eno Sarris

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Additional info for My Book Of Number Games 1-70 (Kumon Workbooks)

Sample text

Suppose f,g E L, E,F ~ S: En F = 0, E not ~-null, f >-E g, f = 9 on F, f ~EuF g. Since L is bounded for ~, there exist u,1 E X such that u ~E f ~E I, u ~E 9 ~E I, u ~F f ~F I and u ~F 9 ~F I.

Talking about n-th degree dominance amounts to skipping n - 1 levels downward of the first ladder and working with a single positive operator which is the composition of all positive operators in-between. Talking about dual characterizations of n-th degree dominance amounts to an analogous skipping upward. 25 "Direct" and "Indirect" Duality B(O) y(O) .... 1 A(l)' A(l) B(l) 1 y(l) .... A(2) I I ~ u(O) ~ A(12) B(2) y(2) .... I I I I B(n) y(n) .... Figure 2 .. U(l) A(12)' U(2) I I I I ~ u(n) Iterated orderings.

Finally, note that a converse result to Lemma 1 can be readily established. 2 Dynamic Consistency We now move on to dynamic consistency. ::E and E is not The names of the two properties above, as well as the formal specification of Weak Substitution, are taken from Myerson (1986). Weak Substitution is (at least apparently) a very mild property. The interpretation is clear: if the DM would not choose 9 over I should she learn that E has occurred, and she would not choose 9 over f should she learn that F has occurred, then she should be able to conclude that 9 is no better than I even before learning which of the two disjoint events has occurred.

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