In biblical scripture ζωή zoe (Life), and ζάω zao (to live | be alive), are not referring to the same thing. Think biblically.

Romans Chapter 11

Chapter divisions were added to the Bible in circa 1227 AD, and verse numbers were added in the 16th century.

In Romans 9:6-7 Paul began talking about the descendants of Israel, saying that not all the descendants of Abraham are children of Abraham, nor are they "Israel" merely because they are descendants of Israel.

This is the same subject Paul continues with all the way through to the close of chapter 11.

In Romans 11:23-24 Paul said that the descendants (plural) of Israel who are broken off through unbelief will be blessed in Christ and grafted into God's elect people again IF they do not continue in unbelief. 

Paul's choice of words is important, because he did not say when they turn away from unbelief, but IF they turn from unbelief, and turning away from unbelief to faith in Christ has been happening in the cases of individual Jews ever since the Deliverer came out of Zion and made a new covenant with them IN THE DAY HE TOOK AWAY THEIR SINS (Romans 11:26-27).

The same distinction Paul makes in Romans 11:1-7 between (a) the remnant of Israel who have not been cast off; and (b) the descendants who have been broken off, Paul is still making in Romans 11:28-29, when he says,

"As concerning the gospel, they (those who are broken off) are enemies for your sakes: but as touching the election, they (the remnant) are beloved for the fathers’ sakes. For the gifts and calling of God are without repentance."

Paul is reiterating not only the fact that God has not cast away His people (Israel) because there remains a remnant (Romans 11:1-7), but also the fact that it is due to the descendants of Israel who are broken off through (their) unbelief) that salvation came to the Gentiles (Romans 11:11 & 17),

and Paul is also reiterating what he said in Romans 9:6-7 (where he began talking about this subject): that not all the descendants of Abraham are children of Abraham, nor are they "Israel" merely because they are descendants of Israel.

Paul is not saying in Romans 11:28 that the descendants of Israel who have been broken off (through their) unbelief are nevertheless "beloved for the sake of the fathers" (Abraham, Isaac and Jacob / Israel): 

he is saying that the remnant are beloved for the sake of the fathers, and the rest are enemies of the good news / gospel (because they do not believe) - and this has benefited the Gentiles, because salvation has come to the Gentiles through their unbelief.

Paul also states that for as long as Gentiles are coming into the same spiritual fullness [G4138 pleroma] of the remnant of Israel, the fullness [G4138 pleroma] experienced by every Jew who repents of unbelief is life from the dead, and results in even greater riches for the same Gentiles (Romans 11:12 & 25).

In the day He took away their sins (Romans 11:27), the Deliverer who came out of Zion made a covenant with those who believe (Romans 11:26-27). All Israel who are defined as the remnant of Israel by Paul in Romans 9:6-7 and Romans 11:1-7 is saved in this way, and shall be saved in this way (Romans 11:26-27) - but not those whom Paul does not define as the remnant of Israel.

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