No, it is not a set phrase. In 2009 the Obama white house apparently returned a bust of Winston Churchill that had been on loan since the September 11 attacks. The British government offered to let Obama keep it for another 4 years to which he seems to have replied "thanks but no thanks".

So, saying that Obama had no room for Churchill in the White House is simply a reference to this story, not applicable to other presidents or deceased historical figures.

What does “the man who had ‘no room for Churchill’ in the White House” mean? Is it a set phrase or just a turn of words?
The task says:


  Show that if some function $\;f(z)={1\over g(z)}$, where
  $g\not\equiv0$ is an       entirely analytic function, then the
  isolated singularities of $\;f$ are exactly zeros of $g$ and namely
  are the poles, that have the same orders as the orders of the
  corresponding zeros of $g$.


As I understand it correctly (relying on what Wikipedia says) the notation $g\not\equiv0$ means that $g$ is never equal to $0$, that means for any $z$, which would be the same if we said that $g$ doesn't have zeros. But the taks asks us to prove that these not existing zeros are the singularities of $\;f(z)$. 

Is there something wrong with my knowledge of mathematical notation or with the taks itself?
