Yes, I am familiar with limits. What I mean is—if you say “f(x) goes to zero as x goes to zero”, then you are implying (in a non-mathematical sense) that we are evaluating f(x) in a region about zero—that is, we are interested in the behavior of f(x) close to x=0.
Edit: More to the point, if I say “g(f(x)) goes to zero as f(x) goes to infinity”, then f(x) better not be (known to be) bounded above.
Yes, I am familiar with limits. What I mean is—if you say “f(x) goes to zero as x goes to zero”, then you are implying (in a non-mathematical sense) that we are evaluating f(x) in a region about zero—that is, we are interested in the behavior of f(x) close to x=0.
Edit: More to the point, if I say “g(f(x)) goes to zero as f(x) goes to infinity”, then f(x) better not be (known to be) bounded above.