To the OP. Words of Jedsus Only.
Matthew 25:46
(46) And these shall go away into everlasting punishment:[kolasis] but the righteous into life eternal.
The Greek word "kolasis" translated "punishment" in this vs. occurs one other time in the N.T. , In jn 4:18.
1 John 4:18
(18) There is no fear in love; but perfect love casteth out fear: because fear hath torment[kolasis]. He that feareth is not made perfect in love.
He that fears has kolasis/torment and is not made perfect. The "torment" is NOT corrective as some folks argue.
According to Jesus "aionios" the Greek word correctly translated "eternal" does in the fact mean "eternal."
“aionios” occurs 72x in the N.T.
“aionios” is translated 'world' only 5 times in the N.T.
“ainios” is translated eternal 42 times in the N.T.
“aionios” is translated everlasting 25 times in the N.T.
Jesus used “aionios” twenty eight [28] times, Jesus never used “aionios” to refer anything common, ordinary or mundane which was not/could not be “eternal.”
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In the following verses aionios is defined/described as eternal, everlasting, eternity etc, by paralleling or juxtaposition with other adjectives or descriptive phrases.
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…..Some people claim that “aionios” never means eternity/eternal because it sometimes refer to something which is not eternal.
However, “aionios” is never defined/described, by adjectives or descriptive phrases, as meaning a period of time less than eternal, in the New Testament, as it is defined/described as "eternal" in the following verses.
…..Jesus used “aionios” twenty eight [28] times. He never used “aionios” to refer to anything common, ordinary or mundane that was not or could not be eternal.
…..In the following ten verses Jesus defines “aionios” as “eternal.”
[1] Luke 1:33
(33) And he shall reign [basileusei][Vb] over the house of Jacob for ever; [aionas] and of his kingdom [basileias][Nn] there shall be no end.[telos]
In this verse the reign/basileusei, which is the verb form of the word, is "aionas" and of the kingdom/basileias, the noun form of the same word, "there shall be no end.” “Aionas” by definition here means eternity.
[2] John 6:58
(58) This is the bread that came down from heaven. Your ancestors ate manna and died, but whoever feeds on this bread will live forever.[aionios]
In this verse Jesus juxtaposes “aionios life” with “death.” If “live aionios” is only a finite period, a finite period is not opposite “death.” Thus “aionios” by definition here means “eternal.”
[3] John 10:28
(28) I give them eternal [aionios] life, and they shall never [aion] perish; no one will snatch them out of my hand.
In this verse Jesus parallels “aionios” with “[not] snatch them out of my hand.” If “aionios” means “age(s), a finite period,” that is not the opposite of “[not] snatch them out of my hand’” “Aionios life” by definition here means “eternal life.”
[4]John 3:15
(15) That whosoever believeth in him should not perish, but have eternal [aionion] life.
[5] John 3:16
(16) For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting [aionion] life.
In these two verses Jesus parallels “aionion” with “should not perish.” Believers could eventually perish in a finite period, thus by definition “aionion life” here means eternal or everlasting life.
[6]John 5:24
(24) Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting [aionios] life, and shall not come into condemnation; but is passed from death unto life.
In this verse Jesus parallels “aionios” with “shall not come into condemnation” and “passed from death unto life.” “Aionios” does not mean “a finite period,” by definition here it means “eternal,” unless Jesus lets His followers come into condemnation and pass into death.
[7]John 3:36 He that believeth on the Son hath everlasting [aionios] life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.
In this verse Jesus juxtaposed aionios life with “shall not see life.” If aionios means an indefinite age that is not opposite “shall not see life” By definition aionios means eternal.
[8]John 4:14 But whosoever drinketh of the water that I shall give him shall never [ου μη/ou mé] thirst; but the water that I shall give him shall be in him a well of water springing up into everlasting [aionios] life.
In this verse Jesus paralleled aionios with “shall [ου μη/ou mé][fn] never thirst.” If aionios means an indefinite age that is not opposite “shall never thirst.” By definition aionios means eternal. See footnote [fn] on “ou mé” below.
[9]John 6:27
(27) Labour not for the meat which perisheth, but for that meat which endureth unto everlasting [aionios] life, which the Son of man shall give unto you: for him hath God the Father sealed.
In this verse Jesus contrasted “aionios [eternal] meat” with “meat that perishes” If aionios means an indefinite age that is not opposite “meat that perishes.” By definition aionios means eternal.
[10]John 8:51
(51) Very truly [amen amen] I tell you, whoever obeys my word will never [ou mé eis ton aiona][fn] see death."
In this verse Jesus juxtaposes “unto aion” with “never see death.” By definition “aion” means eternity.