I A quick question regarding the application of Aleph numbers to reality

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Aleph numbers represent different sizes of infinity and do not limit the concept of infinity itself. They arise from Cantor's distinction between countable and uncountable infinities, expanding the understanding of infinity in mathematics. While Aleph numbers are primarily theoretical, their implications raise questions about their application in measuring aspects of reality, such as space and time. The discussion highlights a curiosity about whether these mathematical concepts can have practical scientific relevance. Overall, Aleph numbers remain a fascinating topic in the exploration of infinity.
Happyman101
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Hi everyone,

I have a quick question about Aleph numbers. Are they even possible? By containing infinity to a finite set, isn’t that essentially disproving the infinity in the first place? Can they be used in an actual scenario’s, or are they just purely hypothetical? Can they be used to measure space, time, and dimensionality? Universes and/or multiverses? Are they scientifically possible?

Thanks for the help.
 
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Aleph numbers are a way of counting types of infinities and have nothing to do with limiting the infiniteness of any infinity.

When infinity first came into existence in math, it was simply infinity.

However, after Cantor described countable infinities vs uncountable infinities the notion of types of infinities was born and so was the idea of wondering about other types of infinities.

https://en.wikipedia.org/wiki/Aleph_number
 
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Greetings, I am studying probability theory [non-measure theory] from a textbook. I stumbled to the topic stating that Cauchy Distribution has no moments. It was not proved, and I tried working it via direct calculation of the improper integral of E[X^n] for the case n=1. Anyhow, I wanted to generalize this without success. I stumbled upon this thread here: https://www.physicsforums.com/threads/how-to-prove-the-cauchy-distribution-has-no-moments.992416/ I really enjoyed the proof...

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