Following up my three-way classification of paradoxes,[1] I want to argue that paradoxes involving infinity are always of type-3, that is, the result of ill-posed problems or inappropriate ways of taking limits. (Much the same position is defended in the comments thread by Bill Carone). In fact, I’d argue for the following general principle, applicable to all models relevant to human decisionmakers.

Whenever a result, true for all finite n, is strictly[2] reversed for the infinite case, the problem in question has been posed incorrectly

To defend this, I rely on the premise that we are finite creatures in a finite universe. If a mathematical representation of a decision problem involves an infinite set, such as the integers or the real line, it is only because this is more convenient than employing finite, but very large bounds, such as those derived from the number of particles in the universe. Any property that depends inherently on infinite sets and limits, such as the continuity of a function, can never be verified or falsified by empirical data. Since we are finite, any result that is true for all finite n is true for us.
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