If the physical universe cannot contain infinity (which is a wise default position to have in the absence of extraordinary evidence), there will be limits at which our infinity-laden mathematical models will fail. Our simple problems were meant to explore these limits. We may find that the infinity-based predicted outcome can still hold, but for different reasons (as in the first problem); or that the infinity-based predicted outcome is wrong, and we have to reason differently to reach qualitatively different conclusions (second and third problems).

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