The following assertion is trivial in ZFC, or even in much weaker theories. Is it also true in ZF?

(I couldn't find it in the Consequences site so far.)


  If $A$ is an infinite set such that $A$ can be mapped onto $A\times 2$ then $|A\times 2|=|A|$


The problem is that we cannot necessarily choose from every fiber of $f$, so we cannot construct an injection from $A$ to $f^{-1}(A\times\lbrace 0\rbrace)$, which will prove the assertion.

While I'm on the topic, is it possible for a D-finite set to have such property? It is possible for a D-finite set to be surjected onto a larger set than itself, but what about that large?


Question: Have to set multiple displays on every start
Answer: I had a similar problem which I solved quite easily. Although I've a different video card  it might works for you.

I've set an .xprofile file in my home directory with the following content:

xrandr --output LVDS1 --mode 1366x768 --primary
xrandr --output VGA1 --mode 1280x1024 --left-of LVDS1


I think the lines are quite self explaining and you could easily modify it so that it fits your situation. A graphical way to setup your screens using XrandR is ArandR

The settings will be applied when you log in.