Under ZFC, the real numbers can be well-ordered. So, there is some ordinal number whose cardinality is that of the continuum. Is there a standard notation for this number?
For example, the first infinite ordinal is usually denoted $\omega$, and the first uncountable ordinal is usually denoted $\omega_1$. But unless we appeal the continuum hypothesis (or something just as presumptuous), $\omega_1$ may not have cardinality of the continuum.
Here is a related question, which is just my curiosity at work: Do we know whether there is such thing as a least and/or greatest ordinal with cardinality of the continuum?
P.S. One last recreational-math question: Are there any other well-known measures of a number's size besides ordinals and cardinals?