You probably read my “One Man’s Modus Ponens” page, where I quote a Timothy Gowers essay on proof by contradiction and he says (and then goes on to discuss two ways to regard the irrationality of √2 as compared with complex numbers):
...a suggestion was made that proofs by contradiction are the mathematician’s version of irony. I’m not sure I agree with that: when we give a proof by contradiction, we make it very clear that we are discussing a counterfactual, so our words are intended to be taken at face value. But perhaps this is not necessary. …
...Integers with this remarkable property are quite unlike the integers we are familiar with: as such, they are surely worthy of further study.
...Numbers with this remarkable property are quite unlike the numbers we are familiar with: as such, they are surely worthy of further study.
You probably read my “One Man’s Modus Ponens” page, where I quote a Timothy Gowers essay on proof by contradiction and he says (and then goes on to discuss two ways to regard the irrationality of √2 as compared with complex numbers):
Thank you Gwern! This was it.