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. Apr 24, 2015 · The infinite monkey theorem states that if you have an infinite number of monkeys each hitting keys at random on typewriter keyboards then, with probability 1, one of them will type the complete works of William Shakespeare.
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