Immortality; How Would it Work?

Physical immortality is impossible to obtain. However, I'm asking to know so my writing isn't exaggerated or too weak about the subject. I think a character would know if they were immortal after being shot in the eye.

 

I dunno, there was the cheerleader from Heroes. She was testing her immortality, and actually managed to get killed once, but then the coroner took the (IIRC) tree branch out of her skull, allowing her brain to heal/regenerate. The issue might be in doubt for some time.

 

In order to be truly immortal, their body must have a cap in terms of physical ageing. In mortal life DNA loses the end blocks whenever it divides to create new cells. Eventually this gets to a point where vital information is lost. Hence the body degrading in old age.

A theme with my immortal characters is that they stress how it costs the person the ability to die peacefully.

I wondered if she was invulnerable to long term damage rather than immortal in the strictest sense. I say this because of the reasons above.