I have also realized that all of your memories could be false, and it worried me for a while, until i realized that it doesn't matter. following the existential theory that it is my thoughts, and perceived experiences that make the world real, at least to me. The fake memories I was given (so long as they don't contradict my current experiences) are my life and are just as real as anyone else's [velociraptor air quotes] "reality"
You can't prove your existence. Watch The Matrix,one of its themes was a brain in a vat thought experiment:
"Since the brain in a vat gives and receives exactly the same impulses as it would if it were in a skull, and since these are its only way of interacting with its environment, then it is not possible to tell, from the perspective of that brain, whether it is in a skull or a vat. Yet in the first case most of the person's beliefs may be true (if he believes, say, that he is walking down the street, or eating ice-cream); in the latter case they are false. Since the argument says one cannot know whether he or she is a brain in a vat, then he or she cannot know whether most of his or her beliefs might be completely false. Since, in principle, it is impossible to rule out oneself being a brain in a vat, there cannot be good grounds for believing any of the things one believes; one certainly cannot know them."
Heck,we could be living in a simulated reality in which we are actual computer programs(aka we have no element in the real world).We cannot prove our existence(I'm agnostic).
I can prove that the world is not a figment of my imagination because, if it was I would be able to make my worst enemies burn with the ferocity of a thousand suns, get us out of this world-wide debt crisis, and establish world peace just by imagining and willing it. But, no matter how hard I try it does not happen so it is safe to say that the world is not a figment of my imagination because if it was then all these things would have happened but sadly it has not. That is my view on this subject
But, see, when we say a fragment of my imagination, I don't think we mean that someone consciously creates a mental image of you, me, everyone in this group or in a town, but we simply hypothesize that this whole world could be a creation a someone's subconscious, and on that you have personally no control, which would explain why you're not able to destroy you're enemies or get us out of the economic crises, so you're argument on why we can't be product of imagination would fall. Descartes though, said nothing can be known for certain, everything's related to the thoughts, excetera, but he also made a distinction between res cogitans and res extensa. The first would be the reality related to his "I think, therefore I am", free, conscious of course, and with no limits. The second would be the reality consisting in matter, limited and unconscious. And he proves the existence of the res extensa by stating that there are two things that can not be denied by the mind because the mind itself doesn't live in them,and they are time and space. We exist because we occupy a place in space and time. We think outside space because thoughts have no limitations and outside time because thoughts have to be free. So not being able to know those things, we are therefore unable to deny them. Moreover, we said mind is subjective and conscious, which is obvious, but we also know that the matter itself is objective therefore it can't be conscious of herself. If I am just a slice of your imagination and so is the world around me, how can something conscious like your mind produce something unconscious like the external reality? You can't create something you don't know or don't understand. It's like when philosophers try to prove that god doesn't exist: how can we, limited being, imagine something illimited, how can we, imperfect, think, picture and know perfection which is one of god's conditions of existence?
Not possible. The only thing that I can be certain of is my own existence. For all I know YOU are a figment of my imagination! *dun dun duuuuuuuuuuuuuuun*
I'm not a figment of your imagination, although there's no way I could prove that to you. Nor could you prove that you are not a figment of mine.