I'm having trouble understanding the statement:
If $\kappa$ is a cardinal, $\aleph$ is any $\aleph$-number, and if $\kappa\leq\aleph$ then $\kappa$ can be well ordered as well.
I understand the concept of well-ordering a set of cardinal numbers (any set of cardinal numbers is in fact well-ordered by the relation $\le$) but I'm not sure if I have a proper understanding of what exactly it means to well-order an individual cardinal number.
I know that to each cardinal number there is associated a unique ordinal number and an ordinal number is set consisting of ordinal numbers strictly less than it so it's well-ordered and so to say $\kappa$ is well-ordered, is all that we mean is that the ordinal number that this cardinal numbers is associated to is well-ordered?
If what I'm saying is correct, aren't all cardinal well-ordered? What do we need this condition for then: $\kappa \le \aleph$ (where $\aleph$ is a well-orderable cardinal)?
Sorry if I'm confusing you too.