"Diagonalization" strikes again. There's a lesson here kids: when you can't prove something, "diagonilization" is the proof-tool of choice. Sure, if you includ

"Diagonalization" strikes again. There's a lesson here kids: when you can't prove something, "diagonilization" is the proof-tool of choice. Sure, if you include it, you won't have proven anything either, or useful, or correct, but you might just get a PhD. (For those who are curious: diagonilization is a proof that takes the form: "Imagine you did this impossible thing. With the result of doing that impossible thing, now try and do this other, reasonable thing. You can't! So whatever properties I can derive from not being able to do this other, reasonable thing are true. (Please ignore that the first step is impossible, and focus on my brilliance in discussing the second, reasonable step.)" That is, in a nutshell, the diagonilization "proof". The rest of the details are just there to make it look like it's actually logic or math. Best not to look too closely. Also, you'll be shocked, SHOCKED to learn that not a single result in the real world relies on the diagonilization proof (though a lot of real-world PhDs would no doubt be affected by it's loss). sigh Mathematicians are idiots when they try and do logic. Stick with numbers, boys.