Testing for presence of element on a page

Testing for presence of element on a page

I think I'm making a jQuery syntax error, have a look at the code below.

if ($('#this-selector-is-on-the-page')){ // check for existence of selector
      // Want to do this stuff, and it is executing, so OK.
}
if ($('#this-selector-is-NOT-on-the-page'){ // check for existence of selector
      // Don't want to do this stuff on this page, but it is executing anyway.
}

What is my mistake?