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The parable of the brides and the bridegroom explains this.
Mat 25:5 While the bridegroom tarried, they all slumbered and slept.
We see in 1Co that the dead are referred to as sleeping.
1Co 15:51 Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed,
1Co 15:16 For if the dead rise not, then is not Christ raised:
1Co 15:17 And if Christ be not raised, your faith is vain; ye are yet in your sins.
1Co 15:18 Then they also which are fallen asleep in Christ are perished.
I believe that you and Beps are both saying the same thing about the meaning of the "last day" and "last days". The last day means the last day of a given period.
Joh 7:37 In the last day, that great day of the feast, Jesus stood and cried, saying, If any man thirst, let him come unto me, and drink.
In this verse we see it was the last day of Jesus being with the disciples before His death and resurection. Then in the following verse we know that it is talking about a period of more than one day but toward the ending of a given period (or age).
Act 2:17 And it shall come to pass in the last days, saith God, I will pour out of my Spirit upon all flesh: and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams: