The aim of this blog post is to prove that if $\kappa$ and $\gamma$ are two infinite cardinals then $\kappa$ + $\gamma =\max(\kappa,\gamma)$. It should be pretty clear that it suffices that we prove $\kappa+\kappa=\kappa$ for any infinite cardinal $\kappa$. We can proceed using Zorn’s lemma: For an infinite set $X$ with cardinality $\kappa$, consider the set of all pairs $(M,f)$, where $M$ is a subset of $X$ and $f$ is a bijection from $2\times M\to M$. Now we can partially order this set by extention on both coordinates. Further it is pretty clear that every chain has an upper...