Set Theory – Symbol for the Cardinality of the Continuum

cardinalsnotationset-theory

The usual symbol for the cardinality of the continuum (i.e. the real numbers) is Fraktur $\mathfrak{c}$. However, I recall some sources also using $\aleph$ (with no subscript). This usage is not mentioned in Wikipedia or Mathworld, but I found some support for it over Google.

Is the $\aleph$ notation standard?

Best Answer

I have seen the use of $\aleph$ and $\mathfrak{c}$ as well the explicit $2^{\aleph_0}$.

If you're uncertain, it's best just to add "We denote the cardinality of the continuum by ...".

(Edit: I should perhaps clarify, that $\aleph$ is not uncommonly used in Israel in basic set theoretic courses. Some of which are taught by respected set theorists, although not all of them. It is true, however, that in a more advanced capacity this usage disappears.)