is written . Its cardinality is written .

Alternatively, for every infinite cardinal that can be well ordered, an index can be defined as the ordinal of the well ordered set of all infinite cardinals that precede . Then it can be proved by transfinite induction that if in the index of then

Informally, the aleph function is a bijection from the ordinals to the infinite cardinals that can be well ordered.Formally, in ZFC, is not a function, but a function-like class, as it is not a set (due

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