Sum and product of two infinite cardinals
= Sum and product of two infinite cardinals
For infinite cardinals $\kappa$ and $\lambda$, the <axiom of choice> and the <square of an infinite cardinal> give
$$
\kappa+\lambda=\kappa\lambda=\max\{\kappa,\lambda\}.
$$
The maximum is a lower bound for both operations, while both are bounded above by respectively $\mu+\mu$ and $\mu^2$, where $\mu=\max\{\kappa,\lambda\}$.