König's theorem

There is also a proposition in graph theory called König's lemma.

In set theory, König's theorem states that if I is a set and m_i and n_i are cardinal numbers for every i in I, and

then

(Of course this is trivial if the cardinal numbers m_i and n_i are finite and the index set I is finite. If I is empty, then the left sum is the empty sum and therefore 0, while the right hand product is the empty product and therefore 1.)

[As it stands, this article is something of a stub. Maybe some history and a proof and some special cases of interest and applications could be added.]

Encyclopedia Home Page

König's theorem