3 ms·
Even weirder is the Conway base 13 function, which not only is discontinuous everywhere, but its range when restricted to any interval is the entire set of real
by xigoi 2y ago
Even weirder is the Conway base 13 function, which not only is discontinuous everywhere, but its range when restricted to any interval is the entire set of real numbers (so its graph “fills up” the entire plane).
https://en.wikipedia.org/wiki/Conway_base_13_function https://en.wikipedia.org/wiki/Conway_base_13_function
- seanhunter 2y agoJohn Conway was amazing. Such a loss that he died of COVID. As well as the game of life, surreal numbers and other famous things, he also produced one of my favourite lesser-known proofs ever - the proof that 91 is the smallest number that looks prime, but isn’t https://youtu.be/S75VTAGKQpk?si=IW791RaeCsXSOrrK https://youtu.be/S75VTAGKQpk?si=IW791RaeCsXSOrrK “This is an important theorem and a discovery that I’m very proud of”.
- seanhunter 2y agoReply to add: Reading about that function it really breaks my brain. It’s incredibly strange to think a function could satisfy the intermediate value property on every interval and yet not be continuous. That really doesn’t feel like it should be possible.
- youoy 2y agoThank you for the 91 proof! I didnt know about that
- dhosek 2y agoI always have to check which John Conway this is. Thankfully John H. and John B. had different middle initials even if they didn’t use them.