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

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SUMMARY

Aleph numbers represent a classification of different sizes of infinity, as established by Georg Cantor. They do not limit the concept of infinity but rather categorize it into countable and uncountable infinities. The discussion clarifies that Aleph numbers are theoretical constructs and are not applicable in practical scenarios such as measuring space, time, or dimensions in the universe or multiverse. Their existence is rooted in mathematical theory rather than empirical science.

PREREQUISITES
  • Understanding of set theory and its terminology
  • Familiarity with Cantor's work on countable vs. uncountable infinities
  • Basic knowledge of mathematical infinity concepts
  • Awareness of theoretical mathematics versus empirical science
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  • Research Cantor's Theorem and its implications on infinity
  • Explore the concept of countable vs. uncountable sets in set theory
  • Investigate the philosophical implications of infinity in mathematics
  • Examine the applications of Aleph numbers in theoretical mathematics
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Mathematicians, philosophers of mathematics, students studying set theory, and anyone interested in the theoretical aspects 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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If there are an infinite number of natural numbers, and an infinite number of fractions in between any two natural numbers, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and... then that must mean that there are not only infinite infinities, but an infinite number of those infinities. and an infinite number of those...

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