Hello 88,
It is God who chose those whom He wanted to save and that not based on anything that we have done or will do, but by God's sovereign selection. Consider the following:
"he saved us, not because of righteous things we had done, but because of his mercy. He saved us through the washing of rebirth and renewal by the Holy Spirit,"
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Not only that, but Rebekah’s children were conceived at the same time by our father Isaac. Yet, before the twins were born or had done anything good or bad—in order that God’s purpose in election might stand: not by works but by him who calls—she was told, “The older will serve the younger.”Just as it is written: “Jacob I loved, but Esau I hated.”
What then shall we say? Is God unjust? Not at all! For he says to Moses,“I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.”
It does not, therefore, depend on human desire or effort, but on God’s mercy. For Scripture says to Pharaoh: “I raised you up for this very purpose, that I might display my power in you and that my name might be proclaimed in all the earth.”
Therefore God has mercy on whom he wants to have mercy, and he hardens whom he wants to harden.
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"The inhabitants of the earth whose names have not been written in the book of life from the creation of the world will be astonished when they see the beast, because it once was, now is not, and yet will come."
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Regarding the above scripture demonstrates that everyone that God selected, their names were written in the book of life before the world began and that there were names that were not written. However, those whose names that were written must still have faith and remain in that faith. According to what Jesus said, it is possible for names to be blotted out of the book of life.
"Like them, the one who is victorious will be clothed in white garments. And I will never blot out his name from the book of life, but I will confess his name before My Father and His angels."
Regarding the above, the promise of not blotting an indiviuals name out of the book of life, is to the believer who is victorious. Therefore it would be the opposite for those who are not victorious.