The question was about existing, not about being real.
By the way, you make a logical error:
This is a non-sequitor. Your conclusion can be justified if you can show that his imagination is outside the thoughts of the author or the reader. Since this is not the case (imagination is thought) you have not shown that you don’t exist.
If you do anything, or have any attribute, you exist. Perhaps not as a physical human, but that wasn’t the question now, was it? 
yeah, so… where is the line drawn? I mean we could say you exist as that which doesn’t exist. Gotta stop it somewhere, since its your question Beeble, tell us. Only then we can move on to more enjoyable philosophizing 
(hey, any excuse to smoke up and quote Nietzsche)
O.K. you win. In retrospect, this question probably should have been posted in IMHO. I thought I could remember more philosophy than what turned out to be the case. Oh, well.
-Beeblebrox
“What to do if you find yourself stuck in a crack in the ground underneath a giant boulder you can’t move, with no hope of rescue. Consider how lucky you are that life has been good to you so far. Alternatively, if life hasn’t been good to you so far, which given your current circumstances seems more likely, consider how lucky you are that it won’t be troubling you much longer.”
Seeing as the author passed away recently, but we the readers still exist, that leaves Beeblebrox in a state not dissimilar to Schrodenger’s cat.
So what is the half-life of a three-armed ex-Galactic president, anyway?
I believe you exist. Therefore, for my purposes, you exist. Whether or not you think you exist for your purposes doesn’t matter to me, because my particular reality is fulfilled.
I’m so hip I have difficulty seeing over my pelvis.
I believe you exist. Therefore, for my purposes, you exist. Whether or not you think you exist for your purposes doesn’t matter to me, because my particular reality is fulfilled.
I’m so hip I have difficulty seeing over my pelvis.
You realize, of course, that this post of yours is the reason I got very little sleep last night.
You don’t want to know what kinds of dreams you get when you fall asleep at 3 in the morning contemplating the existence of nonexistence.
I’ve come to the conclusion that even that which exists as that which doesn’t exist exists. It also doesn’t exist. I have also concluded that I need a Guiness now.
The only reason I posted that was to make Beeble say whether he wanted us to prove whether his body existed, his consciousness existed, or his universe.
I always find it funny when I think about how our minds as a species have evolved so much that we can actually keep ourselves awake with questions so utterly irrelevant in evolutionary/survival terms.