Which continued the sentence from the previous line.
I.e. "If you are not studying holomorphic functions, you are studying complex variables."
I am sorry, @user64742, that this was not clear.
Alternatively, the sentence could be rewritten as the more stilted "If one is not studying holomorphic functions, one isn't doing complex analysis. One is, I suppose, engaged in the study of complex variables, which is more elementary."
in complex analysis, if you can integrate a function, then that function is differentiable.
That is one of the things which makes complex analysis interesting: roughly speaking, once a function is known to be complex differentiable (i.e. it has a derivative) on some domain, then it must have complex derivatives of all orders.
If a function has a primitive (i.e. it has an antiderivative, i.e. it has an integral), then that primitive must be differentiable, therefore the original function has derivatives of all orders.
@RoddyMacPhee When you write collary do you mean corollary. (I wanted to edit the post - thinking that it is a typo. But then I noticed that you used the same word more than once, so I wasn't entirely sure.
Just multiply Fermat on both sides by d ... you get the collary.
cor·ol·lar·y /ˈkôrəˌlerē,ˈkärəˌlerē/ Learn to pronounce noun a proposition that follows from (and is often appended to) one already proved. adjective forming a proposition that follows from one already proved.
Just to clarify, my comment wasn't meant as a criticism. Various minor edits) correcting typos, improving MathJax, etc.) are part of the effort to improve the posts on the site.
OP changed their number @MartinSleziak I've got news for them, answer only adds a few more multiplies ... first two digits( hence exponents) are pinned in a range spanning 5329 wide. only the bases will change possibly, within 50% of that range...
Hi, there is someone who keeps "attacking" a recent question of mine. Yesterday he deleted his answer and all his comments. Now he has undeleted his old answer and updated it with a new answer. I had made comments on his previous post which may no longer be relevant to this answer. Can he just keep harassing me like this?
This is a quote from his updated answer: "(This seems like a bit of a wasted exercise; the whole below is contained in Lang, if one is willing to do just a bit of work. Moreover, the OP says to pretend he is a "dimwit" for the purpose of explaining this. But explaining math to dimwits is like mudwrestling with a pig. Not only does it accomplish nothing, but you get dirty and the pig likes it.)"
Do you see anything wrong with my question that can justify this sort of reaction on their part?
@user64742 that's correct. It's a sort of bug from the system because the holomorphic-function tag is there and so one might think "hmm I'm gonna add it because... " and then you click on save edit and then after it's approved, then there's nothing. so why to 'have' such tag if doesn't work to classify post? and makes us believe that's it's there! that's not fair
@quid quid's superpowers :Dhaha. // quid, the questions that I tagged with holomorphic-function will never be holomorphic-functions? or can you do something about it if the synonym gets cancelled?
@kiko hello! Do you want to speak to a moderator privately? If yes, no problem, I can set it up. If no, just go ahead and formulate your concern.
@Isabellatrix yeah, fear me! ;-) After the synonym gets cancelled, they could be tagged like this manually. But there is no dedicated function for this. Worse still there, is no trace of the earlier attempt. That's a thing I don't like. It's almost completely "silent"; there is no way to trace which instances of a tag are genuine and which are synonym retags, there is merely a global number.
