I was watching a video: https://youtu.be/HeQX2HjkcNo?t=1171 and had a quesion on the incompleteness proof.
In the video, he introduces us to the statement: "There is no proof for the statement with Godel number $g$"
Then he says that the trick is that the Godel number of that statement is $g$. My question is how can you be sure that such a number $g$ exists? Since the conjecture itself has $g$ in it, wouldn't the Godel number be dependent on $g$? More specifically, I believe that the Godel number of any statement that has a number $x$ is greater than $x$. Is that not always the case?