What does c mean in the following question on cardinality?

Question

I found a question in Modern Real Analysis by William P. Ziemer. The question can be found in Section 2.1 Question 1. It goes: Use the fact that $\mathbb N =$ {$ n: n = 2k$ for some $k \in \mathbb N$} $\cup$ {$ n: n = 2k+1$ for some $k \in \mathbb N$} to prove $c \cdot c = c$. What could they be referring to by c? I know it has something to do with cardinality because the question continues as follows: Consequently, $card(\mathbb R^n) = c$ for each $n \in \mathbb N$.

Answer 1

Based on the structure of the question, it seems likely that the dot is just the product operator, which in the case of cardinalities means that $c \cdot c = card(\mathbb{R}) \cdot card(\mathbb{R}) = card(\mathbb{R} \times \mathbb{R})$, i.e. the product of two cardinalities is the cardinality of the Cartesian product of the sets.