identify the statement that does not hold in a complete ordered field K and provide a counterexample, or an argument as to why it does not hold. it's Z ⊂ K in this case. (i) ∀b ∈ K, ∃a ∈ K, 4ab = b. (ii) ∀a ∈ K, ∃b ∈ K, [(6ab = b) ∧ (b ≠ 0)]. (iii) ∀a∈ K, [0 < a < 1 ⇒  a2 < a].

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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identify the statement that does not hold in a complete ordered field K and provide a counterexample, or an argument as to why it does not hold. it's Z ⊂ K in this case.

(i) ∀b ∈ K, ∃a ∈ K, 4ab = b. (ii) ∀a ∈ K, ∃b ∈ K, [(6ab = b) ∧ (b ≠ 0)]. (iii) ∀a∈ K, [0 < a < 1 ⇒  a2 < a].

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