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Axiom 3 in Section 2.4 of your text asserts the existence of an indifference probability for any gamble. Axiom 3 is the following. Axiom 3

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Axiom 3 in Section 2.4 of your text asserts the existence of an indifference probability for any gamble. Axiom 3 is the following. Axiom 3 (Continuity): For any gamble g in G, there is some probability OK 6 [0, 1], such that g N (OK 0 a1, (1 - Ci) 0 an). Axiom 4 is the following Axiom 4 (Monotonicity): For all probabilities or, B e [0, 1], (0' 0 a1, (1 - 0') an) t ([30 311(1 - [3) 3.) if and only if Ci 2 B. Prove that the indifference probability from Axiom 3 is unique using Axiom 4

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