Exactly! Which means aion doesn't mean forever or eternity.
So shall it be at the end of the world: the angels shall come forth, and sever the wicked from among the just, And shall cast them into the furnace of fire: there shall be wailing and gnashing of teeth. (Mat 13:49-50 KJV)
Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels: (Mat 25:41 KJV)
In these two passages the words "world" and "everlasting" are the same Greek word. Why do you suppose they didn't translate it everlasting in both places?
Context determines meaning.
Mat 13:49 So it will be at the end of the age. The angels will come out and separate the evil from the righteous
Mat 13:50 and throw them into the fiery furnace. In that place there will be weeping and gnashing of teeth.
In Matt 13:49, the context clearly indicates an end of a period of time and therefore
cannot mean "eternal" or "everlasting."
Mat 25:41 “Then he will say to those on his left, ‘Depart from me, you cursed, into the
eternal fire prepared for the devil and his angels.
...
Mat 25:46 And these will go away into
eternal punishment, but the righteous into
eternal life.”
It stands to reason from verse 46, that if the punishment of the wicked is temporary, then so is life for the righteous. The context is speaking of final things, an indefinite period of time. That is, unlike Matt 13:49, there is nothing that happens afterwards; it just is.
We must also take into account what is said elsewhere:
Rev 14:9 And another angel, a third, followed them, saying with a loud voice, “If anyone worships the beast and its image and receives a mark on his forehead or on his hand,
Rev 14:10 he also will drink the wine of God's wrath, poured full strength into the cup of his anger, and he will be tormented with fire and sulfur in the presence of the holy angels and in the presence of the Lamb.
Rev 14:11 And
the smoke of their torment goes up forever and ever, and they have no rest, day or night, these worshipers of the beast and its image, and whoever receives the mark of its name.”
Rev 20:10 and
the devil who had deceived them was thrown into the lake of fire and sulfur where the beast and the false prophet were, and
they will be tormented day and night forever and ever.
The language is the same of those who worship "the beast and its image" and receive "a mark," and of the devil, the beast, and the false prophet--"day and (or) night;" "forever and ever;" "torment(ed)." The repetition, particularly of
aion, is used for emphasis and strongly suggests eternality.
It is the exact same phrase as here:
Rev 1:6 and made us a kingdom, priests to his God and Father, to him be glory and dominion
forever and ever. Amen.
Rev 4:9 And whenever the living creatures give glory and honor and thanks to him who is seated on the throne, who lives
forever and ever,
Rev 4:10 the twenty-four elders fall down before him who is seated on the throne and worship him who lives
forever and ever. They cast their crowns before the throne, saying,
Rev 5:13 And I heard every creature in heaven and on earth and under the earth and in the sea, and all that is in them, saying, “To him who sits on the throne and to the Lamb be blessing and honor and glory and might
forever and ever!”
Rev 7:12 saying, “Amen! Blessing and glory and wisdom and thanksgiving and honor and power and might be to our God
forever and ever! Amen.”
Rev 10:6 and swore by him who lives
forever and ever, who created heaven and what is in it, the earth and what is in it, and the sea and what is in it, that there would be no more delay,
Rev 11:15 Then the seventh angel blew his trumpet, and there were loud voices in heaven, saying, “The kingdom of the world has become the kingdom of our Lord and of his Christ, and he shall reign
forever and ever.”
Rev 15:7 And one of the four living creatures gave to the seven angels seven golden bowls full of the wrath of God who lives
forever and ever,
Those are all in reference to God and to Christ, and I don't think anyone would argue that it doesn't mean eternal in these instances. And also of this one, speaking of believers:
Rev 22:5 And night will be no more. They will need no light of lamp or sun, for the Lord God will be their light, and they will reign
forever and ever.
(All ESV.)
All of that supports the translation of
aion in Matt 25:41, 46 as eternal or everlasting.