How would you interpret them, if you think they are not separated?
I think the crux of the chapter is verse 15.
Romans 11:15
15 For if the casting away of them be the reconciling of the world, what shall the receiving of them be, but life from the dead
There is so much said in this one verse:
1) The people of Israel were cast away from something/someone
2) That casting away led to the reconciling the world (gospel)
3) The people of Israel will be received again to something/someone
4) Receiving them will lead to the raising of the dead (the resurrection)
...and we know that the resurrection includes
all those who are "in Christ", which we know as "the body of Christ".
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In chapter 11, Paul shares with us an analogy using an olive tree and branches.
He calls the people of Israel "natural branches" and calls gentile believers "wild branches", saying the natural branches are broken off from
their good olive tree while the wild branches are grafted into
that good olive tree...but there will come a time when the natural branches will be grafted again into
THEIR good olive tree (the olive tree gentile believers are currently grafted onto).
Romans 11:24
For if thou wert cut out of the olive tree which is wild by nature, and wert grafted contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be grafted into their own olive tree
There's only
one good olive tree: the one the natural branches
came from that the wild branches are currently nourished by. So they're not separate, the natural branches are simply cast off for now in punishment.
If we relabeled the analogy we can see this:
Good olive tree = Israel, of which Messiah is King
Natural branches = (blood descents) the people of of Israel
Wild branches = gentile believers in Messiah