Web Reference: Mar 31, 2026 · 6 Informally, I would like to find an infinite product of rational numbers that evaluates to a nonzero rational number such that the multiplicity of each prime in the numerator is finite, while on the denominator there are an infinite number of primes with unbounded multiplicity. I will make this more precise below. It is just what you want it to be, as long as it makes sense mathematically. We can talk about $+\infty$ and $-\infty$ in the extended real line, and about $\infty$ in the extended comlex plane. We can talk about cardinalities of sets, or about ordinals, too. The concept of "infinity", meaning "not finite" has very different and various meanings and uses in mathematics. Dec 10, 2023 · Here's a proof by induction that the resistance of a finite version of this ladder with $\ n\ $ rungs is indeed homogeneous of degree $1$ in the variable $\ R\ .$ Taking the limit as $\ n\rightarrow\infty\ $ (assuming it exists $\left.\right.^\color {red} {\dagger}$) then shows that the resistance of the infinite ladder depicted in Figure $2 ...
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