Here are scholarly explanations which better define "αἰωνίου" or "aiōniou" (and their derivatives).
Encyclopedic Dictionary of the Bible: Eternity: The Bible hardly speaks of eternity in a philosophical sense of infinite duration without beginning or end. The Hebrew word olam, which is used alone (Ps. 61:8) or with various prepositions (Ge. 3:22; 13:15, etc.) in contexts where it is traditionally translated "forever," means, in itself, no more than "for an indefinitely long period." Thus, me-olam does not mean "from eternity," but "of old" (Ge 6:4, etc.). In the N.T., aion is used as the equivalent of olam.
The New Testament in Modern Speech, by Dr. R. F. Weymouth: Eternal: Greek: "aeonion," i.e., "of the ages." Etymologically this adjective, like others similarly formed, does not signify "during," but "belonging to" the aeons or ages.
The Interpreter's Dictionary of the Bible (vol. IV, p. 643): Time: The O.T. and the N.T are not acquainted with the conception of eternity as timelessness. The O.T. has not developed a special term for "eternity." The word aion originally meant "vital force," "life;" then "age," "lifetime." It is, however, also used generally of a (limited or unlimited) long space of time. The use of the word aion is determined very much by the O.T. and the LXX. Aion means "long distant uninterrupted time" in the past (Luke 1:10), as well as in the future (John 4:14).
Ellicott's Commentary on the Whole Bible (Matt. 25:46): Everlasting punishment-life eternal. The two adjectives represent the same Greek word, aionios-it must be admitted (1) that the Greek word which is rendered "eternal" does not, in itself, involve endlessness, but rather, duration, whether through an age or succession of ages, and that it is therefore applied in the N.T. to periods of time that have had both a beginning and ending (Rom. 16:25), where the Greek is "from aeonian times;" our version giving "since the world began." (Comp. 2 Tim. 1:9; Tit. 1:3) -strictly speaking, therefore, the word, as such, apart from its association with any qualifying substantive, implies a vast undefined duration, rather than one in the full sense of the word "infinite."
Triglot Dictionary of Representative Words in Hebrew, Greek and English [this dictionary lists the words in this order: English, Greek, Hebrew] (p. 122): Eternal (see age-lasting). (p. 6): English: age-lasting; Greek, aionios; Hebrew, le-olam.
Encyclopedic Dictionary of the Bible: Eternity: The Bible hardly speaks of eternity in a philosophical sense of infinite duration without beginning or end. The Hebrew word olam, which is used alone (Ps. 61:8) or with various prepositions (Ge. 3:22; 13:15, etc.) in contexts where it is traditionally translated "forever," means, in itself, no more than "for an indefinitely long period." Thus, me-olam does not mean "from eternity," but "of old" (Ge 6:4, etc.). In the N.T., aion is used as the equivalent of olam.
The New Testament in Modern Speech, by Dr. R. F. Weymouth: Eternal: Greek: "aeonion," i.e., "of the ages." Etymologically this adjective, like others similarly formed, does not signify "during," but "belonging to" the aeons or ages.
The Interpreter's Dictionary of the Bible (vol. IV, p. 643): Time: The O.T. and the N.T are not acquainted with the conception of eternity as timelessness. The O.T. has not developed a special term for "eternity." The word aion originally meant "vital force," "life;" then "age," "lifetime." It is, however, also used generally of a (limited or unlimited) long space of time. The use of the word aion is determined very much by the O.T. and the LXX. Aion means "long distant uninterrupted time" in the past (Luke 1:10), as well as in the future (John 4:14).
Ellicott's Commentary on the Whole Bible (Matt. 25:46): Everlasting punishment-life eternal. The two adjectives represent the same Greek word, aionios-it must be admitted (1) that the Greek word which is rendered "eternal" does not, in itself, involve endlessness, but rather, duration, whether through an age or succession of ages, and that it is therefore applied in the N.T. to periods of time that have had both a beginning and ending (Rom. 16:25), where the Greek is "from aeonian times;" our version giving "since the world began." (Comp. 2 Tim. 1:9; Tit. 1:3) -strictly speaking, therefore, the word, as such, apart from its association with any qualifying substantive, implies a vast undefined duration, rather than one in the full sense of the word "infinite."
Triglot Dictionary of Representative Words in Hebrew, Greek and English [this dictionary lists the words in this order: English, Greek, Hebrew] (p. 122): Eternal (see age-lasting). (p. 6): English: age-lasting; Greek, aionios; Hebrew, le-olam.

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