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,

  1. 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.

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