Question

Let S be the set of all continuous functions f: [0,[infinity]) → R. Let R be the relation defined on S by (f,g) ∈ R iff f(x) is O(g(x)).

Is R reflexive?

Answer 1

The relation R is not reflexive in this case.

Step-by-step explanation:

The relation R is not reflexive in this case. A relation is reflexive if (f, f) is in R for all functions f in the set S. In this case, for R to be reflexive, we would need f(x) to be O(f(x)). However, this is not always true for all continuous functions f(x). There exist continuous functions where f(x) is not O(f(x)). Therefore, R is not reflexive.