= Solution
The <set> of all <functions> from a <set> of size $\mathfrak c$ to another <set> of size $\mathfrak c$ has size $\mathfrak c^{\mathfrak c}$. <Cardinal exponentiation> and the law $(\kappa^\lambda)^\mu=\kappa^{\lambda\mu}$ give
$$
\mathfrak c^{\mathfrak c}
=(2^{\aleph_0})^{\mathfrak c}
=2^{\aleph_0\cdot\mathfrak c}
=2^{\mathfrak c}.
$$
Therefore
$$
\boxed{|\mathbb R^{\mathbb C}|=2^{\mathfrak c}.}
$$
The <lower bound> can also be seen by taking characteristic <functions> of all <subsets> of $\mathbb C$. <Cantor's theorem> makes this strictly larger than $\mathfrak c$, unlike the continuous-function space in the next part.
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