- #1
Son Goku
- 113
- 21
Just an ideal question, possibly asked before, but is there an example of a Set which has cardinality of [tex]\aleph_{2}[/tex]?
Higher Cardinals: Example of Set with Cardinality Aleph2?
- Context: Graduate
- Thread starter Son Goku
- Start date
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SUMMARY
The discussion centers on the existence of a set with cardinality \(\aleph_{2}\). It is established that under the Generalized Continuum Hypothesis (GCH), the set of all functions \(f:\mathbb{R}\rightarrow\mathbb{R}\) possesses cardinality \(\aleph_{2}\). This conclusion highlights the dependency on the assumptions made regarding set theory and cardinality.
PREREQUISITES- Understanding of cardinality in set theory
- Familiarity with the Generalized Continuum Hypothesis (GCH)
- Knowledge of functions and mappings in mathematics
- Basic concepts of real numbers and their properties
- Research the implications of the Generalized Continuum Hypothesis (GCH)
- Explore examples of sets with different cardinalities
- Study the properties of functions from \(\mathbb{R}\) to \(\mathbb{R}\)
- Investigate the relationship between cardinality and set theory axioms
Mathematicians, set theorists, and students studying advanced topics in set theory and cardinality.
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