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In maths, what is aleph-zero?

the cardinality of the set of all countable ordinal numbers

the cardinality of the set of all natural numbers

the base value of the natural logarithm

the cardinality of the set of real numbers

The aleph numbers are a sequence of numbers used to represent the cardinality of infinite sets that can be well-ordered. The cardinality of the natural numbers is aleph-zero, the next larger cardinality is aleph-one, then aleph-two and so on. The concept and notation are due to Georg Cantor, who defined the notion of cardinality and realized that infinite sets can have different cardinalities.

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