- #1
lolgarithms
- 120
- 0
Why is "almost certain" := EXACTLY 1? Shouldn't it be 1 minus an infinitesimal (reciprocal of an infinite cardinal) for a dense space? (Why aren't surreal numbers acceptable?)
"Almost Certain = 1" is a mathematical expression that represents a probability of an event occurring with a high level of certainty. Surreal Numbers are a type of number system that extends the real numbers to include infinitesimal and infinite values.
While Surreal Numbers offer a more comprehensive number system, they also bring along complications and inconsistencies in mathematical operations. Rejecting Surreal Numbers allows for a simpler and more consistent mathematical framework.
Yes, Surreal Numbers have been used in certain areas of mathematics and theoretical physics. However, their use is limited due to the aforementioned complications and inconsistencies.
Yes, there are various alternative number systems that have been proposed, such as Hyperreal Numbers and Superreal Numbers. These systems also extend the real numbers but have different properties and applications.
Scientists and mathematicians use other tools and techniques, such as statistical analysis and probability distributions, to handle probabilities without Surreal Numbers. These methods are well-established and have been proven to be effective in various fields of research.