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 youāll 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 cutānāpaste it into its own post ā thereās no quota for posting and the bar really isnāt that high.
The post Xitter web has spawned soo many āesotericā right wing freaks, but thereās no appropriate sneer-space for them. Iām talking redscare-ish, reality challenged āculture criticsā who write about everything but understand nothing. Iām talking about reply-guys who make the same 6 tweets about the same 3 subjects. Theyāre inescapable at this point, yet I donāt see them mocked (as much as they should be)
Like, there was one dude a while back who insisted that women couldnāt be surgeons because they didnāt believe in the moon or in stars? I think each and every one of these guys is uniquely fucked up and if I canāt escape them, I would love to sneer at them.
(Credit and/or blame to David Gerard for starting this.)
Wouldnāt f(x) = x^2 + 1 be a counterexample to āany entire (differentiable everywhere) function that is never zero must be constantā? Or are some terms defined differently in complex analysis than in the math I learned?
Iāve 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 (Liouvilleās theorem) is that a bounded entire function must be constant.
Or Picardās 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.
Oh, I didnāt know that!
Who is flaviat? I donāt see that handle on this lemmy or Greg Eganās 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
now it works! I do not understand the two sentences āIāve never heard of a function being called entire out of complex analysis. But still, it (what? - ed.) is zero at i.ā
I believe those sentences can be paraphrased as, āThe term entire function is only used in complex analysis. The function f(z) = z^2 + 1 is zero at z = i.ā
Thanks, i donāt speak english natively
the poster is referring to the function
f(z) = z^2 + 1Itās 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 āstrongerā than it existing in R.
Edit: wikipedia pages on holomorphism and analyticity (did I spell this right) are good
entire always means holomorphic on the whole complex plane
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