And g(x) is 1/x

So f(x) <= g(x)

But g(x) is divergent. Thus, but the comparison test, this says absolutely nothing about convergence.

Basically, the covergent thm just says that if you have something less than a finite number (i.e. convergent), it is also a finite number. If you have something greater than an infinite number (divergent), it is also infinite.

But what if you have something greater than a finite number? You can't really tell if that's finite or infinite. And if you have something less than an infinite number? You can't really say if that is still finite or infinite.