Want to wade into the sandy surf of the abyss? Have a sneer percolating in your system but not enough time/energy to make a whole post about it? Go forth and be mid: Welcome to the Stubsack, your first port of call for learning fresh Awful you’ll near-instantly regret.
Any awful.systems sub may be subsneered in this subthread, techtakes or no.
If your sneer seems higher quality than you thought, feel free to cut’n’paste it into its own post — there’s no quota for posting and the bar really isn’t that high.
The post Xitter web has spawned soo many “esoteric” right wing freaks, but there’s no appropriate sneer-space for them. I’m talking redscare-ish, reality challenged “culture critics” who write about everything but understand nothing. I’m talking about reply-guys who make the same 6 tweets about the same 3 subjects. They’re inescapable at this point, yet I don’t see them mocked (as much as they should be)
Like, there was one dude a while back who insisted that women couldn’t be surgeons because they didn’t believe in the moon or in stars? I think each and every one of these guys is uniquely fucked up and if I can’t escape them, I would love to sneer at them.
(Credit and/or blame to David Gerard for starting this.)
Wouldn’t f(x) = x^2 + 1 be a counterexample to “any entire (differentiable everywhere) function that is never zero must be constant”? Or are some terms defined differently in complex analysis than in the math I learned?
It’s worth noting that, unlike a real function, a complex function that is differentiable in a neighborhood is infinitely differentiable in that neighborhood. An informal intuition behind this: in the reals, for a limit to exist, the left and right limit must agree. In C, the limit from every direction must agree. Thus, a limit existing in C is “stronger” than it existing in R.
Edit: wikipedia pages on holomorphism and analyticity (did I spell this right) are good
I’ve never heard of a function being called entire out of complex analysis. But still, it is zero at i.
A fact that AI gets wrong.
flaviat explained why your counterexample is not correct. But also, the correct statement (Liouville’s theorem) is that a bounded entire function must be constant.
Or Picard’s little theorem, which says that if an entire function misses two points (e.g. is never 0 or 1), then that function must be constant.
Who is flaviat? I don’t see that handle on this lemmy or Greg Egan’s mastodon account, and Egan just re-tooted someone who gives x^2 + 1 as a counterexample.
Does this link work for you to see the comment? https://awful.systems/comment/9163259
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