Part IA, Numbers and Sets
Quotations:
For all N = "For any natural number in the whole world..."
Counterexample = "If your evil opponent picks some number..."
Solved = "But 'Ah ha'!"
"One bad number kills it."
"Instantly dead..."
"...and we're dead." (these two in context of proofs)
"Proof: well, we're done, aren't we?"
This is a proper contradiction now, not the feeble overkill we had before."
"The proof of this is: 'stare at it a bit'."
"When we want to prove sqrt(2) irrational, what we say is: 'Suppose it is rational; mumble mumble, contradiction."