Sorry, are you familiar with the mathematical concept of limit? Saying that “f(x) goes to zero as x goes to zero” does not imply the nonsensical belief that “x goes to zero”.
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.
Sorry, are you familiar with the mathematical concept of limit? Saying that “f(x) goes to zero as x goes to zero” does not imply the nonsensical belief that “x goes to zero”.
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.