Wait a minute. Do you mean alive in the sense that:
1. A copy of your physical self and all your memories and your consciousness are still there, so you effectively are alive and still exist?
or
2. Because a copy of your physical self with an exact consciousness exists, you somehow live on having experiences in the new clone as if nothing happened?
No for the first one I guess, and for the second one, yes, you're dead, but I don't think you even need to use the reasoning you used. I think people want to believe that if your consciousness and physical self were copied to somewhere else, you would start having experiences in that other body, but it's tied to the first "you" only.
It's as simple as this, really.
But now:
Teleporter scenario, person goes into teleporter, he is destroyed. He is now dead and everything is dark for him. (Let's pretend that's how being dead is)
His atoms are beamed to another location, where they are rebuilt to form a replica of the conciousness and body of the person that walked into the teleporter.
The replica will now be conciousness #2, as #1 is gone.
Conciousness #2 believes that it is conciousness #1, and nobody notices that conciousness #1 is gone.
So basically, for the person that goes in (Conciousness #1) he will see the teleporter start, then he will cease to exist.
The person that comes out (Conciousness #2) will be the same as #1, except he still exists and remembers everything before and after the teleportation.
It's strange to think of, and I'm not entirely sure if it's the correct way to think.
For some reason, I feel that it's impossible that conciousness #1 can be teleported without being permanently destroyed.
But now when I think about it even more, I realize that our conciousness is in the end a physical configuration.
It should be possible to send it just like you can send regular atoms, thus keeping conciousness #1.
I love thinking about this.
Yeah, this helps a lot. The "copying" method of teleporting, if you want to call it that, is really scary to think about. If you can move the actual particles...problem solved.