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I've thought about this too. Remember, the smith who made all the rider's blades said she refused to give Brom another sword after he lost his. I think Maud, the werecat, and Solumbum knew what was going to happen in the future, and they stole Brom's sword, stashing it under the tree for Eragon...
Wait a minute. Something mind-blowing just came to me. What if... what if Brom was really Eragon's father, not Morzan? It would make sense. Brom wouldn't have missed selena so much when she left if they were just acquaintances....what if Eragon and Murtagh are half-brothers? Selene is mother to both, but they had different fathers? Therefore, if Brom's sword really is under the Minoa tree, it would be Eragon's Iheritance.
More proof: When Brom told Eragon that he was in Hiding, wouldn't it make sense that of anywhere, he would choose Carvahall, where he could watch his son grow up, and protect him if a threat ever revealed itself? How does Brom know so much about Eragon's history? His Parentage? Where he comes from?
And Then, in Angela's shop, she remembered that Selena's fortune wasn't a good one. What if Angela saw that she would have to choose between two lovers? That would make more sense still. If She chose Brom, was pregnant with Eragon, and went to Carvahall to let Brom raise him, because she knew that Morzan was still persuing her, and if her found out about Eragon, would surely kill him? All questions that could possibly lead to Brom being Eragon's Father, and the sword being his. Of course, It's probably not going to be all "Oooooh looky, a sword."
Chris probably has something big planned for it.

off topic but how do you get those flame swords so fast? they are awesome

Murtagh already said in the second book that the third dragon was male. I don't see why that question was there in the first place.

As for the whole Brom being Eragon's father thing...I'd be greatly disappointed if this were true.

Now...for the name...that's a hard one. I personally think that it's going to depend on who the rider is and their background, as well as how attached they are to the dragon. So I really have no guesses.

^^; No I don't think I'm being so critical. Perhaps I should fix that though. It's just that I'm not exactly a HUGE fan of the inheritance series, yet I tend to know more about it than half my obsessed friends. o.o That's very disappointing.

Honestly I mean it as no insult or anything, I just tend to like to point those things out when they are overlooked. It's just Murtagh went on to say how the dragons would fight to mate with saphira (or something like that).

Perhaps I should have done it in a more tasteful manner, and for that I do apologize. Though this was quite roundabout. Ha ha ^^;

I'm rooting for Thorn...>.> Probably because I love murtagh. ^^; He's just always been the most appealing character to me. I can relate with him so well, though thankfully not becase of the abuse factor.

As far as how Saphira feels about it...I have absolutely no idea. It's hard to say how she would react. So, I'm still just gonna root for Thorn.

I suppose so... Though I still go for Thorn because that means that more than likely Murtagh will survive through the third book and I'll be happy as happy can be. ^-^ Yay!

Edit: Hmm...I needa revamp my looks.

Imma voting for Thorn... Saphira might be a bit sorry for Thorn, because he wa forced to swear allegiance int he Ancient language... I dunno. XP
You know, screw my theory. @.@