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Aleph-zero (ℵ0)
This is a finite set of fragments belonging to round 0 of Genesis period.
The name Aleph-zero (ℵ0) comes from set theory: it is the cardinality (or size) of the set of all natural numbers. It represents the smallest level of infinity and is the smallest infinite cardinal number.
The concept of Aleph-zero is fundamental in understanding different sizes of infinity. It was introduced by Georg Cantor, who founded set theory and explored the notion of infinite sets and their cardinalities. Aleph-zero is used to denote the size of any set that can be put into a one-to-one correspondence with the natural numbers, meaning the set is countably infinite. Examples of sets that have a cardinality of Aleph-zero include the set of all integers, the set of all even numbers, and the set of all rational numbers.
Cantor's work also showed that not all infinities are equal; for example, the set of real numbers has a larger cardinality than Aleph-zero, often referred to as the cardinality of the continuum. This larger infinity cannot be matched one-to-one with the natural numbers, indicating a fundamentally different size of infinity.
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