If you have an infinitesimal chance of succeeding at something, but you do it an infinite amount of times, what is the probability that you succeed at least once?
2026-04-06 07:39:06.1775461146
What is the chance of an infinitesimally small chance happening over infinite tries?
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Probability based on infinitesimals is a well-established subject with a vast publication list. Indeed it is possible to make sense of statements like "infinitely many trials, each with infinitesimal chance of winning, can have appreciable overall probability". This approach was pioneered by de Mises and formalized by Edward Nelson. The approach is "radically elementary" in the sense that it does not require complex developments in measure theory as other approaches to probability on continuous spaces do. Just to mention a recent article, you could consult this.