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QUESTION
Consider the function f: defined on positive integers with f(n) = n "flipped" as a mirror image into a decimal. For example, f(5) = .5, f(418) =...
- Consider the function f: defined on positive integers with f(n) = n “flipped” as a mirror image into a decimal. For example, f(5) = .5, f(418) = .814, and f(1000) = .0001. Define a relation R on the positive integers as (m, n) ∈ R if and only if f(m) ≤ f(n). For example, (5, 418) ∈ R because .5 ≤ .814 but (418, .923) ∉ R because .814 > .329. Is R a partial order? Either provide a proof to show that this is true or provide a counterexample to show that this is false.
