Answered: how that if Λ ∈ Rn and if it meets:

Math

Advanced Math

how that if Λ ∈ Rn and if it meets:

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

show that if Λ ∈ Rn and if it meets:

• ≿ a weak order as to Λ

• (strict dominance) if a_i > b_i ∀i ∈ {1,2,3,...,n} ⇒ a ≻ b

• (continuity) a ≻ b, b ≻ c ⇒∃λ ∈[0,1]. ∋.(λa+(1−λ)c)∼b ⇒∃f ordinal value function representing the preferences of the decision maker.

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