“The axioms aren’t things you’re arbitrarily making up, or assuming for convenience-of-proof, about some pre-existent thing called numbers. You need axioms to pin down a mathematical universe before you can talk about it in the first place. The axioms are pinning down what the heck this ‘NUM-burz’ sound means in the first place—that your mouth is talking about 0, 1, 2, 3, and so on.”
Ok NOW I finally get the whole Peano arithmetic thing. …Took me long enough. Thanks kindly, unusually-fast-thinking mathematician!
Ok NOW I finally get the whole Peano arithmetic thing. …Took me long enough. Thanks kindly, unusually-fast-thinking mathematician!