OP, I'm in the same situation. While I agree it's a little bittersweet, you should also be very proud that you've gotten your kids to this point and they're clearly independent and ready to launch! I'm a little nostalgic myself, but also very excited to start the next chapter in my life. It's wonderful to be in a position where you can reinvent yourself (if you want) or engage in new interests, or just about anything. Embrace this time!
