In this link, Division of cardinals, someone asks a question about cardinal division and references a Wikipedia page about it. The Wikipedia page does not give a reference to their statement, but I'd really like to know one. Does anyone know specifically (preferably book and page number) where I can find this and a proof?
Answer
This follows from the fact that cardinal multiplication is not very interesting for infinite cardinals. Namely, if $\kappa$ and $\mu$ are infinite, $\kappa \cdot \mu = \max(\kappa,\mu)$. Thus, if we're given $\lambda$ and $\kappa$ we may always solve the equation in variable $\mu$
$$ \kappa \cdot \mu = \lambda $$ if and only if $\kappa \leq \lambda$. Indeed, if $\kappa \leq \lambda$, then
$$\kappa \cdot \lambda = \max(\kappa,\lambda) = \lambda.$$ On the other hand, if $\kappa > \lambda$
$$\kappa \cdot \mu = \max(\kappa,\mu) \geq \kappa > \lambda.$$
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