If Jesus's death was not eternal, then how can it be substitutionary for the eternal deaths of humans? Sinful humans are judged and sentenced to eternal death. But did Jesus experience eternal death? If so, how?  If not, how then can it be considered substitutionary for our deaths?

How do those who teach penal substitution explain this?
N - Assume that the total number of people who will ever live (besides Jesus) is N, a finite number.
ω - Assume that redeeming the smallest sin costs an infinite amount, equal to omega, the hyper-real number.
E - Assume that the most evil person who ever lived committed a number of sins equal to E. Given that our lives are finite, the number of sins that can be committed is finite.
N⋅E⋅ω - Multiply these values together to get the upper limit on the cost of redeeming all the sins of the world. This cost is infinite, but linear in omega.

All Sin ≤ N⋅E⋅ω


Jesus is the "King of kings" and "Lord of Lords". To me, that sounds like at least infinity squared, or ω². Jesus spent between two and three days in the grave (since a part of a day counts as a whole day in Hebrew usage, I am told). Assume the lower figure of two days. That makes Jesus payment equal to 2⋅ω²:

Jesus' Payment = 2⋅ω² &gt;&gt; N⋅E⋅ω ≥ All Sin 


Since Jesus' value is so great, the fact that he only spends a finite amount of time in the grave does not prevent him from making a payment greatly in excess of the cost of our sin. This is because for any finite multiplier M, no matter how big, ω² >> M⋅ω. If this makes no sense, read about how to integrate Greens functions and call me in the morning.

For more on the hyperreal number system and how to perform arithmetic, algebra, limits, integration, and differentiation, see:

https://www.math.wisc.edu/~keisler/calc.html

Admittedly, this is not how most supporters of penal substitutionary atonement would answer, but the important point is that the infinity of our sin is smaller than the infinity of his love, and since we have a well-established mathematical framework for comparing materialistic infinities, there must also be one for comparing spiritual infinities.