The only thing living forever would do for me is make me even more bored and sarcasic. Knowing I'm immortal, I'd just do whatever I want and just lose any ability to care I have left, So not much would really change to be honest. F f f f f
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Living forever you are always learning more about the world around you. Weather you want to or not you are always changing and your beliefs are changing with you. They are not necessarily changing in to different sets of beliefs but growing with you. Yes, Your beliefs could over time change in to something totally different and you as a person could change so that who you are right now is a distant memory. Chances are you will change who you are but still have the core of your personality stay the same.
Some would consciously choose to alter their lives, perhaps become nicer, more wholesome, even God-fearing. However, even for those who attempt to stay the same, this is the sort of information that can't help but change a person. Virtually everything we learn, by way of the butterfly effect or otherwise, changes our mental and psychological composition. This would be one of the most significant pieces of information one could learn. It's difficult to imagine it not resulting in a significant change, especially over the infinite life span of an immortal being.
Everything evolves and eventually changes course. No one remains the same in a typical human life span. The knowledge we have now is ever changing and if we became immortal we would only eventually come to discover that there are inevitably some things we were never right about. I guess it would also inevitably rely on the person in question to accept the idea of something they had grown to accept to be true, be nothing of what they had thought to be.