#functional analysis

[amimmy]

Me at the wizard conclave (math conference) conjuring some runes in between talks (solving an exercise) to enchant a foreign sorceress (hit on a phd)

[spectrallysequenced]

[positively-knotted]

God I hate analysis. I was ok with (C[0,1], d_inf) not being homeomorphic to (C[0,1], d_1), that made sense. But the fact that it IS homeomorphic to L1[0,1]? No. That's too far.

[a-lesson-you-never-asked-for]

Exam soon… The only thing I’ll be calculating is the tension in the rope I’ll be hanging myself with.

Someone who once studied functional analysis

[datamodel-of-disaster]

Me when the analyst job requires analysing what exactly the job is

[sarahsfixations]

ive always found it interesting that functional analysis is linear. you'd think like linear covers linear relations, things like linear systems. and functions themselves over their domain dont 'look' linear but no together as a function space they are linear and so by taking higher dimensions one can do vector space stuff then the natural question that arises is what is the nonlinear version, so like generally nonlinear operators i suppose.

[cleverclot]

Functional analysis, how much I admire you and how much you try to crush me with the upcoming exam.

[teachsector]

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[speronyx]

does anyone know anything about the mazur intersection property? is it something that's studied a lot?

[poorly-drawn-mdzs]

MDZS Severance AU: Get me out of here.

[amimmy]

Call me norm-attaining the way I be coarsely embedding into that dense subset

[spectrallysequenced]

Literally what is the point of putting this subchapter this early in the book if you have nothing to say about it? That's literally the entirety of that section, why not just put this after the section on the weak topology??? (Book is A Course in Funcitonal Analysis, 1996 by John B. Conway) ((No, not THAT Conway, that's John H. Conway))

[saturnniidae]

Something that kind of frustrates me is how while there's always plenty of conversation about Hiccup's mistreatment by Berk and how things were before and in the beginning of the first movie, people don't seem to understand that obviously while it was partially out of his control due to his weak constitution/physical inability to do certain tasks, Hiccup never really wanted to be like everyone else.

He wanted to be accepted obviously – "I just want to be one of you guys," but we never see him actively wanting to make an effort to change himself to conform to Berk's standards. He wanted to be accepted among his peers as himself, he had his own way of doing things that he refused to change or compromise on, (this is literally shown and stated be a standard behavior; it's why Stoick was so exasperated with him, why their relationship deteriorated as his childhood progressed!!)

It is the very reason everyone hated him so much. When he started doing well in training he was still unhappy because while he was using tricks he learned from interactions with Toothless, he still wasn't doing things the way he wanted, he was finally making Stoick proud but it was only by succeeding in a way expected of a viking of Berk and by working towards a goal he no longer desired to achieve.

He never wanted to be like his peers, to be the ideal viking and perfect son, he just wanted to be himself and be accepted for it.

[aroaceleovaldez]

how Nico functions narratively as a character is always extremely funny to me because he has like, exactly 3 modes: exposition, damsel, and dues ex machina.

Exposition Mode is usually whenever Annabeth (#1 designated exposition character. #2 is Grover or insert mythological figure of the hour here. #3 is Nico) or someone else isn't around to exposition for the present cast. He has an excuse to somehow randomly know everything and everyone, no matter what, especially if it's relevant to the plot. He'll randomly develop new skills or personal arcs purely as an excuse to put him in situations where he can exposition, such as him being able to gain insight into the future/prophecies via ghosts (which is a thing in Greek mythology, but still). This is actually why it's extremely difficult for him to function as a POV character in a stand-alone story or first book of a series, because the way Riordanverse functions, the POV almost always only has as much information as the audience going into things and a secondary character explains information to them as they go along, unless it's later on into a series and it makes sense for the characters and/or audience to know that already. That's why Nico doesn't function well as a POV for TSATS but Will would work fine, because Nico's designated narrative role is Knowing Everything/Everyone, Somehow (particularly relating to the Underworld).

Damsel: he just gets kidnapped a ridiculous amount of times. Also that plus his penchant for passing out means there is ample opportunity for scenarios where Nico, despite being extremely powerful, needs to be rescued. Pairing this with how he's always off doing absolutely anything, absolutely anywhere, and somehow knows everybody, he's a perfect means to push the plot forward with an easy "oh no we need to rescue/protect Nico for the millionth time" side-quest or addition to stakes at hand. Or, similarly, if you need to take Nico out of the equation for a bit because he's too powerful and would fix it immediately: oops he passed out/needs to be protected/is kidnapped/etc.

And then as mentioned before - Deus ex machina, kinda literally. Nico is extremely overpowered for a reason; Because he's the catch-all solution to every problem. Just throw Nico at it. We can BS a new epic power for him that vaguely makes sense and yeah he's just that powerful and will pass out because of it probably. Yeah sure he can rip people's souls out and instakill things. Yeah he can teleport anything anywhere under essentially any circumstances. He'll just be a little sleepy. A lil eepy. He needs to take a lil nap. It's fine.

Basically. Solution to literally every situation in the Riordanverse: Throw Nico at it. Just throw Nico at it. It'll make sense. It'll work. Unless he's the primary POV in a stand-alone novel, short story, or first book in a series. Then it won't make any sense because you suddenly have to backtrack like 2/3 of Nico's entire narrative functions and suddenly he is Only A Damsel.

[emilinqa]

star trek tos is deeply entrenched in its identity as a 60s tv show for better or for worse (both) but i think retroactively the city on the edge of forever ends up showcasing this more now since its set in a time we can now as 21st century viewers connect with being closer to the time it was produced, rather than the nebulous 23rd. it's interesting because for me i think the single episode informs the way i connect an imagined future to the actual real 1960s the show was written in, particularly in the language and the way relationships between characters are depicted in the way they speak to one another. in that single episode it suddenly feels that the coded language everyone uses, the subtext, the hints and euphemisms is a necessity of the world rather than a feature of the show. and suddenly (for me, at least) that totally shapes the rest of the way i view the rest of the original series. though the way they speak to one another doesn't really tangibly change all that much, when they're placed in the setting of the 1930s the way that kirk and spock speak to each other and about one another entirely shifts.

edith asks kirk in regards to his relationship with spock "I still have a few questions I'd like to ask about you two. Oh, and don't give me that 'questions about little old us' look, you know as well as I do how out of place you two look here." which. well. hello. and later when she asks "Why does Spock call you captain? Were you in the war together?" and kirk says "we... served together" its like yes the obfuscation of their identities and who they are to one another is a necessity of the plot and time travel reasons but i also can't pretend that particular response doesn't color kirks line 2 episodes later in amok time "you've been called the best first officer in the fleet, that's an... enormous asset to me" in a different light. the necessity of secrets and closed doors and frantically having to conceal themselves and their tiny little apartment with a pair of twin beds and ediths "you, by his side as if you've always been there and always will" and "'Captain'? See, even when he doesn't say it, he does" well i can't act like it doesn't change the way i see their enforced professional distance in other episodes, even when they're back safe in their own century. its why The conversation cut from the original harlon ellison script hits seriously i think. it's like a deeply personal confession of desire for a life that could never be: "On my world the nights are very long. The sound of the silver bird against the sky is very sweet. My people know there is always time enough for everything. You would be comfortable there" and a wistful acceptance ("All the time in the world...") in another time in another life in another place it could be but just not this one. spock's endless resignation. well it just changes everything for me. star trek is about the 1960s!!!!!!

[heliomanteia]

I think Nico's ability to survive is less so about his will to live and more so about his refusal (less so personal and more so narrative-wise) to die. Nico, for the lack of a better word, is like a cockroach: you cannot kill him in a way that matters so he survives and keeps haunting the scene.

There was once a marvelous post on Nico's function as a narrative tool and it was so beautifully pointed out that he's a near-omniscient deus ex machina (to simplify) which cannot be overlooked when characterizing him. Nico carries so much narrative weight on his back (which arguably could be an example of either good or bad writing depending on your perspective) that he cannot just go and die.

His road towards healing (though definitely not walked alone/individually) is his own, that's his choice to make as a character, but his disposition as a guy that perseveres resides more within his function, in my opinion.

He's not the tragic prince doomed for self-destruction people often draw him out to be but his capacity for survival is also not a product of his continuous work as a character, at least not just that ��� but is rather a result of his narrative function. Simply saying, you cannot, narratively, kill off Nico di Angelo.