I don't do Greek or Hebrew but I am am pretty good at copy and paste...
Gentile-Greek
G1484
ἔθνος
ethnos
eth'-nos
Probably from G1486; a race (as of the same habit), that is, a tribe; specifically a foreign (non-Jewish) one (usually by implication pagan): - Gentile, heathen, nation, people.
In Greek, we have a bunch of non Jewish pagans...
Gentile-Hebrew
H1471
גּי גּוי
gôy gôy
go'ee, go'-ee
Apparently from the same root as H1465 (in the sense of massing); a foreign nation; hence a Gentile; also (figuratively) a troop of animals, or a flight of locusts: - Gentile, heathen, nation, people.
No hint of any covenant/non covenant people there in the Hebrew...So that eliminates the in/out covenant problelm...
There is only Covenant and non-covenant (gentile), and nothing else.
I agree with that...The 'church' is not a covenant (agreement)...It is a free gift, to make Israel jealous
... And since the new covenant is made with the House of Judah and the House of Israel, and the gentiles are inherited by them (adopted),
Israel doesn't adopt anyone...It is Jesus who is doing the adopting...And Jesus doesn't adopt us into Israel...Jesus adopts us into Him...
Rom_3:24 Being justified freely by his grace through the redemption that is in Christ Jesus:
Redemption is in Christ, not in Israel...
Rom_12:5 So we, being many, are one body in Christ, and every one members one of another.
The 'body' is not Israel...The 'body' is Jesus Christ...Saved Jews get into the body just as saved Gentiles are adopted into the body...
Eph_3:6 That the Gentiles should be fellowheirs, and of the same body, and partakers of his promise in Christ by the gospel:
Fellowheirs...Of the 'head' of that body, not fellowheirs of Israel...
Gal_6:15 For in Christ Jesus neither circumcision availeth any thing, nor uncircumcision, but a new creature.
You'll then have to show me where the House of Israel was rejected. The House of Judah, no doubt. But the House of Israel (lo ammi, Not my People) are a different story altogether.
Jer 3:8 And I saw, when for all the causes whereby backsliding Israel committed adultery I had put her away, and given her a bill of divorce; yet her treacherous sister Judah feared not, but went and played the harlot also.
Jer 3:9 And it came to pass through the lightness of her whoredom, that she defiled the land, and committed adultery with stones and with stocks.
Israel along with Judah was rejected, but not forever...
Heb 8:5 Who serve unto the example and shadow of heavenly things, as Moses was admonished of God when he was about to make the tabernacle: for, See, saith he, that thou make all things according to the pattern shewed to thee in the mount.
Heb 8:6 But now hath he obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises.
Heb 8:7 For if that first covenant had been faultless, then should no place have been sought for the second.
Heb 8:8 For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:
Heb 8:9 Not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my covenant, and I regarded them not, saith the Lord.
Heb 8:10 For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
Gentile = Goyim = “out of covenant.”
Whoever is out of covenant, regardless of their lineage, is a Gentile.
Yes, the ‘Greeks’ were out of covenant, both their Hebrew element and the non-hebrew element.