GameObject.Destroy(gameObject); Not Working?

So I've been following a tutorial online (I'm new to the Unity scene), and the teacher uses Destroy (gameObject); Yet every time I run it (it's supposed to destroy the character when I shoot it), nothing happens. The console doesn't give me any errors, nothing else bad happens, it just doesn't disappear. I looked it up, and someone said to do GameObject.Destroy (gameObject); instead. Still, it does the exact same thing. Am I doing something wrong here? Thanks in advance.

My Code:

 #pragma strict

 var Health = 100;

 function ApplyDamage (TheDamage : int) {

     Health -= TheDamage;

     if (Health <= 0) {

         Dead();
     }
 }

 function Dead() {

     GameObject.Destroy (gameObject);
 }