I've thought a lot about this, and realized that there is no continuation in our normal life anyway. What we experience is a huge and omnipresent blind spot because we cannot see the future.

Even 5 minutes from now, you don't know where you'll be, and you will be a completely different person based on the events of that 5 minutes.

Every moment that passes, the you of the moment dies.

What you can have, is a you in the future that remembers and understands the past you. That only happens if you preserve your memories either by not dying, or by preserving your internal memories in some other way.

That's all you get. A copy in the future that remembers, or nothing at all.