Matthew 25:46

The same Greek word (aiônios) is translated everlasting(punishment) and (life) eternal;also in each case the adjective in the Greek text follows the noun the place of emphasis. The adjective aiônios(eternal) = of or belonging to (1) an aiônor period, (a) past, (b) present, (c) future, or (2) to a succession of aiônsor periods. It does not, therefore, in itself="unending." But life eternal, which is "to know the true God and Jesus Christ" (John 17:3), can only be conceived of as unending and infinite; cp. "Art thou not from everlasting, O Lord my God, mine Holy One? we shall not die" (Habakkuk 1:12).

punishment (Greek, kolasis), not "vengeance," but punishment that checks or reforms.