In the first chapter of Hosea, the prophet became the father of three children whose names were given by God. An important but ominous prophecy was conveyed in these names, particularly the last two. The second child was a daughter named Loruhama, which means "not having obtained mercy." The third child was a son named Loammi, which means "not my people." The reason for the first name is given in verse six: for I will no more have mercy upon the house of Israel; but I will utterly take them away. The reason for the second name is given in verse nine: for ye are not my people, and I will not be your God. Hence the names of these children denote the rejection of the House of Israel by God. But the tenth verse provides a consoling prophecy:

Yet the number of the children of Israel shall be as the sand of the sea, which cannot be measured nor numbered; and it shall come to pass, that in the place where it was said unto them, Ye are not my people, there it shall be said unto them, Ye are the sons of the living God.

Thus Israel was given the promise that one day the curses against them would be so far removed that they would become the sons of the living God.

Now the New Testament alludes to the latter verse at least twice. The Apostle Peter referred to it when he said:

But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light: Which in time past were not a people, but are now the people of God: which had not obtained mercy, but now have obtained mercy. - 1Pet 2:9,10

Therefore Peter proclaimed to the believing Jews that the curses of Hosea had been taken from them and that the blessings of Hosea had become theirs. This teaches us what is the path of restoration for the Jews from their rejection in Hosea. It is the Lord Jesus Christ, who is the way, the truth and the life, and no man can come unto the Father but by Him (Jn 14:6).

The Apostle Paul also referred to Hosea 1:10 when he wrote:

What if God, willing to shew his wrath, and to make his power known, endured with much longsuffering the vessels of wrath fitted to destruction: And that he might make known the riches of his glory on the vessels of mercy, which he had afore prepared unto glory, Even us, whom he hath called, not of the Jews only, but also of the Gentiles? As he saith also in Osee, I will call them my people, which were not my people; and her beloved, which was not beloved. And it shall come to pass, that in the place where it was said unto them, Ye are not my people; there shall they be called the children of the living God. - Rom 9:22-26

Here it appears Paul is applying Hosea 1:10 to the Gentiles. Since Hosea obviously wrote the verse with only Israel in mind, it is highly unlikely that Paul intended a prophetic application. Instead, he was adapting the "principle" conveyed in the verse; namely, that formerly rejected people, whether Jew or Gentile, are brought nigh unto God through Christ and Him alone, for there is none other name under heaven given among men, whereby we must be saved. (Acts 4:12).