This recent SMBC comic illustrates the old question of what exactly is you by referencing the Star Trek Teleporter Problem. Do you actually get teleported or does the teleporter just kill you before making a copy of you somewhere else?
Well, the answer that a lot of rationalist seem to accept is Pattern Identity Theory proposed by Hans Moravec (skim the link or do a google search for the theory if you have no idea what I am referring to). I am very sympathetic to this view and it definitely ties with my limited understanding of physics and biology - elementary particles are interchangeable and do not have 'identity', at least some of the atoms in your body (including some of those who form neurons) get replaced over time etc.
This is all fine and dandy, but if you take this view to its logical extreme it looks like a sufficently modified version of you shouldn't actually qualify as you - the difference in the pattern might be as great or greater than the difference in the patterns of any two random people.
Let's say something happens to Eliezer and he gets successfully cryo-preserved in 2014. Then 80 years later the singularity hasn't arrived yet but the future is still pretty good - everyone is smart and happy due to enhancements, ageing is a thing of the past and we have the technology to wake cryopreserved people up. The people in that future build Eliezer a new body, restore the information from his brain and apply all the standard enhancements on him and then they wake him up. The person who wakes up remembers all that good old Eliezer did and seems to act like you would expect an enhanced Eliezer to act. However, if you examine things closely the difference between 2014!Eliezer and 2094!Eliezer is actually bigger than the difference between 2014!Eliezer and let's say 2014!Yvain due to having all the new standard enhancements. Does that person really qualify as the same person according to Pattern Identity Theory, then? Sure, he originates from Eliezer and arguably the difference between the two is similar to the difference between kid!Eliezer and adult!Eliezer but is it really the same pattern? If you believe that you really are the pattern then how can you not think of Eliezer!2014 as a dead man?
Sure, you could argue that continual change (as opposed to the sudden change in the cryo!Eliezer scenario) or 'evolution of the pattern' is in some way relevant but why would that be? The only somewhat reasonable argument for that I've seen is 'because it looks like this is what I care about'. That's fine with me but my personal preference is closer to 'I want to continue existing and experiencing things'; I don't care if anything that looks like me or thinks it's me is experiencing stuff - I want me (whatever that is) to continue living and doing stuff. And so far it looks really plausible that me is the pattern which sadly leaves me to think that maybe changing the pattern is a bad idea.
I know that this line of thinking can damn you to eternal stagnation but it seems worth exploring before teleporters, uploading, big self-enhancements etc. come along which is why I am starting this discussion. Additionally, a part of the problem might be that there is some confusion about definitions going on but I'd like to see where. Furthermore, 'the difference in the pattern' seems both somehow hard to quantify and more importantly - it doesn't look like something that could have a clear cut-off as in 'if the pattern differs by more than 10% you are a different person'. At any rate, whatever that cut-off is, it still seems pretty clear that tenoke!2000 differs enough from me to be considered dead.
As an exercise at home I will leave you to think about what this whole line of thinking implies if you combine it with MWII-style quantum immortality.