- Why does $\lim\limits_{x\rightarrow a}(f-g)(x)=0$ then $f(x)\sim_{x\rightarrow a}g(x)$ false
- and $f(x)\sim_{x\rightarrow a}g(x)$ implies $\lim\limits_{x\rightarrow a}(f-g)(x)=0$ false?
I was given the fact that $f(t)=t \ \& \ f(t)=t^2$ aren't equivalent aroud $0$ but have same limits, but aren't they equivalent as far as they have same limits!
Furthermore I was also given the fact that $f(t)=t \ \& \ g(t)=t+\ln t$ equivalent when $+\infty$ even if their difference is $+\infty$