It looks like other people have covered your questions, but having played Infinite first myself, you might want to now look into the Burial at Sea DLC! It has mixed reviews, but I think it’s great if you’re interested in seeing Rapture before its fall and would like to follow more of Elizabeth’s story (and in the ambiance of Bioshock 1!).
If so, the devs are gonna have to make it unambiguous to explain how Burial at Sea fits into the continuity. Myself, I don't think it's that ambiguious: Comstock and Columbia are erased from existence, and Booker never gives up Anna. So my theory attempts to explain that unambiguous ending with Booker meeting Elizabeth in Rapture.
The truth is, Burial at Sea happens at the same time when Infinite's ending happens. I will go over this chronologically. At the end of the game, Booker successfully escorted Elizabeth to destroy the siphon. Elizabeth now lives outside space and time just like Lutece, and can see through every single door.
Here's the important bit: In the vast ocean of despair and depravity that is Rapture, you're attempting to rescue a single soul, a newly-minted Little Sister named Sally. She's held in captivity
This might, however, be one of the best value offerings the store has put forward since its launch - grabbing the entire collection via Steam would currently set you back more than $75, and you're
Knowing that, the last remaining elizabeth, the main one, the one that can travel through dimensions at will, goes after him to finish the job. But by trying to kill him, she let herself become violent and merciless. She also uses a little girl to manipulate him and doesnt really care what happens to her.
Seriously, can someone explain some reasons why people hated it. From what I gathered for some reason people were butt hurt that the main character, Booker, Dies. For me I have my understanding of what the ending means and it makes sense to me. Personally, I think people hated the ending because it was a mind-♥♥♥♥ kinda like Spec-Ops the line, as people do when they dont understand
The problem with that particular venue of explanation, is that it suddenly ignores the 'infinite possibilities' that choices create. Jack saving the little sisters is just one possibility in the 'multiverse', it is by no means THE definitive possibility (especially since bioshock 1 gives you the option of harvesiting the little sisters rather than saving them).
This lessens the impact of Bioshock Infinite's plot, it's setting, it's ending, it's characters, those character's development, pretty much everything about Infinite. This game wasn't it's own standalone story, it was a stepping stone so that Bioshock might happen and Jack can rescue Little Sisters.
Warning: Massive ending spoilers for BioShock Infinite. Minor spoilers for Burial At Sea. Told in two episodes (which I played back-to-back), Burial At Sea centers on Booker and Elizabeth’s
SvoF.