Consider a set that has integers p and inverses 1/q, infinitely many of both. We are about to form a product of all numbers in this set, with two different arrangements.(adsbygoogle = window.adsbygoogle || []).push({});

Arrange terms, way 1:

For each p (countably many), select 1/q so that q>p, the resulting product term is (p * 1/q) < 1. The supply of p's are exhausted this way, and in addition there are infinitely many left-over 1/q's. As far as I understand (and possibly not), the product of all should be 0.

Arrange terms, way 2:

For each 1/q select p>q, the resulting terms are (1/q * p) > 1 with infinitely many left-over p's. This seems an infinite product.

Missing something? Thanks in advance.

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# Infinite product, arranging of terms

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