The definition of "eternal" that I posted is from Mirriam-Webster's dictionary:
having infinite duration : everlasting; of or relating to eternity; characterized by abiding fellowship with God… See the full definition
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One of the definitions in your source is "in the reign of God" and also "of unseen glory in contrast to the transitory world of the senses":
"in the Reign of God: ζωὴ αἰ. (Orig., C. Cels. 2, 77, 3)
Mt 19:16, 29;
25:46;
Mk 10:17, 30;
Lk 10:25;
18:18, 30;
J 3:15f, 36;
4:14, 36;
5:24, 39;
6:27, 40, 47, 54, 68;
10:28;
12:25, 50;
17:2f;
Ac 13:46, 48;
Ro 2:7;
5:21;
6:22f;
Gal 6:8;
1 Ti 1:16;
6:12;
Tit 1:2;
3:7;
1J 1:2;
2:25;
3:15;
5:11, 13, 20;
Jd 21; D 10:3; 2 Cl 5:5; 8:4, 6; IEph 18:1; Hv 2, 3, 2; 3, 8, 4 al. Also βασιλεία αἰ.
2 Pt 1:11 (ApcPt Rainer 9; cp.
Da 4:3;
7:27; Philo, Somn. 2, 285; Mel., P. 68, 493; OGI 569, 24 ὑπὲρ τῆς αἰωνίου καὶ ἀφθάρτου βασιλείας ὑμῶν; Dssm. B 279f, BS 363). Of the glory in the next life δόξα αἰ.
2 Ti 2:10;
1 Pt 5:10 (cp. Wsd 10:14; Jos., Ant. 15, 376.—SibOr 8, 410 φῶς αἰῶνιον). αἰώνιον βάρος δόξης
2 Cor 4:17; σωτηρία αἰ. (
Is 45:17; Ps.-Clem., Hom. 1, 19)
Hb 5:9; short ending of Mk. Of unseen glory in contrast to the transitory world of the senses τὰ μὴ βλεπόμενα αἰώνια
2 Cor 4:18.—χαρά IPhld ins; δοξάζεσθαι αἰωνίῳ ἔργῳ
be glorified by an everlasting deed IPol 8:1. DHill, Gk. Words and Hebr. Mngs. ’67, 186–201; JvanderWatt, NovT 31, ’89, 217–28 (J).—DELG s.v. αἰών. M-M. TW. Sv.[1]"
The Greek "aionios" and English "eternal" are quite equivalent, but they need to be understood properly.
Eternity is what is timeless or exists outside time. Here is a Greek Orthodox analysis:
In the debate about the theological validity of Christian universalism one sometimes finds discussion about the meaning of the word “eternal” in Matthew 25:46. Christ there says plainly that the unrighteous “will go away into eternal punishment”, and the word here rendered “eternal” is the Greek...
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