It is NOT a dream: The WEDDING RING gives it away.
I have now seen this movie three times. The first time I saw it I thought it was not a dream and he was home. When I saw discussions to the contrary, I saw it again looking for any clues to tell whether he is dreaming the whole time, and questioned the ending thoroughly. It was not until I saw a post about someone saying he is only wearing a wedding ring when he dreams. Multiple people shot it down saying that they saw him wearing it in reality or that he was not wearing it in this dream or that one. My third viewing had me looking for the ring in almost every shot, seeing if his totem ever falls in a dream (Something someone said happened), looking at his children's faces to see if they are the same, etc.
My analysis as follows:
The Wedding Ring:
We start the movie with Cobb in limbo with Saito, he is wearing a ring. Step back to the beginning, he is trying to convince Saito to let him into his mind to help protect it, this takes place in a dream two layers down. He is wearing a wedding ring. Things go south and we wake up in the apartment, where we think an angry mob is really coming down the street. They threaten Saito's life with him thinking it is reality, only for him to discover otherwise. In this entire scene Cobb is wearing a wedding ring. Wake up on the train, NO WEDDING RING. In the hotel suite on the phone with his kids, NO WEDDING RING. On the roof talking to Saito, NO WEDDING RING. France, the architecture university, NO WEDDING RING. The coffee shop in Ariadne's first shared dream, Cobb is wearing his wedding ring, she freaks out. They wake up in the workshop, NO WEDDING RING. They go back under and Ariadne explores the physics of the dreamworld, again Cobb is wearing a wedding ring.
Cobb goes to see Eames, the entire time not wearing a ring. He meets the new chemist, still no ring. The chemist gives him a quick taste of his latest potion, in that scene we get a quick glimpse of his hand with a WEDDING RING. Wakes up, no ring. See the pattern?
So finally, the inception. We are on the plane, we clearly see is not wearing a ring. Level 1, WEDDING RING, Level 2, WEDDING RING, Level 3 WEDDING RING, Limbo he is wearing his WEDDING RING.
After he meets Saito as an old man, the conversation continues past what we saw in the beginning, yet even here he is wearing a WEDDING RING still. Then, when Saito reaches for the gun, we are on an airplane. He is not wearing a wedding ring here.
HERE IS THE KEY. As he is walking through the terminal, no ring, as he is greeted by father in law, no ring, when he gets home and spins his totem, no ring.
In his dreams he is married to Mul still, as she can still exist there. In reality, he knows she is dead and does not wear a wedding ring as he is no longer married. A simple yet easily unnoticed way to test which parts are reality.
Not done there, I investigated another thing, Cobb's totem:
I have seen many posts of people saying his totem falls when he is in others' dreams. This is simply not true. People say it wobbles and falls over in the beginning. I watched and listened closely, Saito spins the top and we hear it spinning as the scene cuts to the young Saito. Then, in the end when we see him old again, he looks down and it is still spinning, he knows he is not in reality and goes for the gun.
When Cobb uses inception on Mul, it continues and never stops. In the hotel after the failed Saito mission, it falls. A funny thing to note is that every scene in which the top spins endlessly he is wearing a WEDDING RING. In the scenes in which it topples, he is not.
Now, the awakening scene. Looks an awful lot like a dream right? Not really. He wakes up on the plane surprised, but everyone is smiling. They woke up from the sedatives, but Cobb and Saito were down in limbo. When they got back, everyone is happy to see he made it, Saito looks just as stunned only backing up the fact that he really snapped back to reality. They are all getting bags, going through customs, etc. Everyone looks at each other with a grin because they know inception worked and that Cobb is finally home. Not very dream-like except that it seems like a dream come true. Had the scene after he and Saito with the gun been him in his home, him on his way to his home, etc, I would think it is a dream. No, he awakens in EXACTLY the place he went to sleep to start inception. You never really know how you get to where you are in a dream do you? Then how does he know he is on a plane and just successfully completed inception on Robert Fischer, the man in front of him?
Finally, the home scene. Looks like a dream? In this case, yes it does. we see the children exactly where they were, doing the same thing, wearing the same clothes. They appear the same age. On my second viewing this was red flag that it was a dream. But on my third viewing I noticed slight differences, such as the kids looking slightly older. The cast list has two sets of kids listed, ones slightly older than the others. They are not voice casts but actual actors in the film. I especially noticed a difference as the camera pans towards the totem, I chose to focus on the back door with the kids. The girl is seen throwing herself on her father, in this scene she looks clearly older than the memory he has of her.
And of course, the totem itself. I watched each spin my third time through. It spun flawlessly for a while, began to wobble slightly, then started a hard wobble then fall. In the final scene it appears to be spinning smoothly for a long time, he probably gave it a lot of power. It starts to slightly wobble, and the screen goes black after it begins a HARD WOBBLE as if it is about to topple, not correct itself.
Conclusion: The movie isn't a dream, Cobb isn't caught in some "limbo that looks a lot like reality." Cobb spends the entire movie trying to get to his kids in reality, why would he settle for shades in a limbo? What proof is there that he is dreaming the whole time? If he is dreaming at the end, where is he dreaming? Limbo? So he goes from talking to Saito to just waking up on a plane, all as a part of a dream in limbo? Really? Think about it.
Nolan would never take the "eeet was aaaaalll a dreeeeaaaammmmm" cliche way out. But the fact that he cut the film before the top falls over does have a meaning. He is planting a seed of doubt in your mind. He uses inception on the audience to have them question the ending. The concept of the movie thus becomes reality to the viewer, a heavy thing to think about and something that hasn't been done before.
But all the evidence points to reality.
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