/sci/ - Science & Math

>>11061295
idk what a "good" question is because I already know the correct answer to it but idk WHY it's the correct answer. I know it's not a difficult question but I'm just stuck. anyway, here goes:

>Let F denote the set of functions from ℕ to ℕ. Define the relation R on F×F as follows:

>(f,g) ∈ R if f(n) ≤ g(n) for infinitely many n∈ℕ

>Which of the following properties does R have?
(have to pick from reflexivity, anti-reflexivity, symmetry, anti-symmetry and transitvity; it's only reflexive BTW)
so during the lecture, when the professor explained it, he used f(n) as a function that maps to 0 when n is an even number. it maps to 1 when n is odd. g(n) is the opposite: maps to 1 when n is even and 0 when it's odd. pic related
so I get that it's reflexive (and thus not anti-reflexive). but I don't get why it's not symmetric. f(n) <= g(n) for infinitely many values of n (= 0, 2, 4, etc.) and g(n) <= f(n) for infinitely many values of n (= 1, 3, 5, etc.)
so IMO fRg and gRf so it's symmetric, right?