Cardinality of [N]^ω: What Does ω Stand For?

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The discussion centers on the cardinality of the set [N]^\omega, specifically addressing the meaning of the symbol ω. In set theory, ω represents the first infinite ordinal number, which is crucial for understanding the structure of infinite sets. The cardinality of [N]^\omega is 2^{ℵ₀}, indicating that it is uncountably infinite. This topic is foundational in advanced mathematics, particularly in the study of ordinals and cardinalities.

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The cardinality of set of [N]^[tex]\omega[/tex] . what does omega stands for?
 
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[tex]\omega[/tex] is usually the http://en.wikipedia.org/wiki/Ordinal_number_(mathematics)" .
 
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