#( i'll get to them! )

[that-g3-artist]

Boomeranger!

get boomeranged

(send me a tri force heroes costume and i'll draw legend in it)

[the-least-undefinable-ordinal]

Hi! Not to give you my literal homework but you were really useful last time and i am s t r u g g l i n g.

I've been stuck on these for days. I've only really worked on the first half of the first one (proving f is injective if C= the inverse image of the image of C) but i suspect that once I get the first one the other one will follow very similarly

Now, I still want to gain the benefit of solving these myself (i.e. not failing my next test), and I think my problem is mostly with my proof technique, so that's my question. Which proof technique would you use to solve these, and can you perhaps give any coy hints as to the general direction of the solution, if you know it.

Obviously you have no obligation to help here but if you maybe wanted to avoid doing some other, harder work.... well.......

The general process in this sort of problem is to first write down (or keep very close in mind) the relevant definitions: in this case they would be that of injective function, surjective function, image and preimage of functions (also what it means for two sets to be equal).

Usually you proceed by proving both sides of the implication, so to prove P if and only if Q, you prove P implies Q and then that Q implies P.

In these two problems it's mostly a matter of manipulating the definitions on each side to arrive at the other.

Taking the first one as an example: assume f is injective and let C be any subset of A, then try to prove by definition of set equality that C = that other thing. At some point during that attempt you may find somewhere to use the hypothesis that f is injective.

Let me know if this helps or not! I have a more detailed proof for these things and I can give more hints, I don't know if I've already given enough though!

[cobraskai]

sorry if you sent a gif request and I haven't posted it yet...supernatural brain rot is winning unfortunately

[whumperofworlds]

Should I do the whump wheel for shits and giggles...?

[lylahammar]

My take on unicorns! I'd really love to make a mythical creature field guide someday, since the Spiderwick Field Guide is what inspired me to start drawing in the first place 🥰

[phantomrose96]

I think we should have a turn of phrase for "I'm not in the right, but I AM annoyed with this situation, so I just need to go bitch to a friend about this before I suck it up and go do the right thing" because more and more I'm finding this is a critical element of functional adulthood.

[pinkravat-art]

i cannot keep my identity secret anymore. I am harrier du bois

[hansoeii]

Ghosts! 👻

[dapper-lil-arts]

If Applejack had whatsapp 🤣🤣🤣

[dustykneed]

survival is an act of rebellion. jim loves you SO MUCH. i hope this finds all of us who need it today. please stay alive so we can make it out together. sending so much love and strength

[biggest-gaudiest-patronuses]

main take aways from Halloween (1978) rewatch:

michael myers is canonically 21??? this bitch should be at the club

*sees tiddies* ***MURDEROUS RAMPAGE NOISES***

that's it that's the movie

outside of the fact that everyone who has sex is murdered by the narrative, this is a surprisingly chill portrayal of female sexuality? these teen girls are horny and actively enjoying Getting It On with their boytoys. no pushy boyfriends sneaking in through their bedroom windows--these ladies are taking the initiative to sneak out and GET SOME. one of them gets laid and then immediately orders her boyfriend to get her a beer. (yes she gets Slashered soon afterward, but so does the boyfriend so honestly, gender equality.) yes the Final Girl is the only one not having sex, but she's not bullied for that, nor are her friends slut shamed except possibly by being murdered by the narrative

actually the only character who is shown being morally condemned on-screen is michael myers. specifically FOR his violent overreaction to other people's sex lives. (people he is spying on). metaphorically, the villain is American Puritanism sticking its judgy nose into other people's business.

aka Michael Myers Is A Republican

but actually the real villain is the doctor. guy's a judgemental, shaming, pathologizing asshole. and he's been in charge of michael's care since he was SIX YEARS OLD? kid never had a chance. i'd go on a killing spree too

also the parents. where are the parents? it's halloween night and all the teenage girls are home babysitting their younger siblings? come to think of it, michael's first victim was his own older sister, whom he killed while she was babysitting him. teen girls are really shouldering a labour burden here. maybe parentification is the true villain

side note: mike commits his first murder wearing a clown costume...which is never referenced again? his 'iconic' costume is a generic mask and wig and jumpsuit, when we coulda had a Killer Clown Michael Myers??? travesty

i like how the Final Girl and her friend casually smoke weed in her car. yeah she's an honor student and her friend is the sheriff's daughter. yeah they smoke weed. so what it's 1978

(to reiterate, mike is 21 and should be at the club. im not saying he shouldn't be rampaging, im saying it's sad that he broke out, tasted freedom for the first time in his life, and immediately snuck back into his childhood home to go rampaging. let's have a remake where he goes to a nightclub and has a few beers. maybe some slutty dancing. then rampage)

oh no he's hot

[trans-androgyne]

I read too many stories of "women" throughout history who lived as men and wore men's clothing getting beaten and arrested for it, sensationalized in the press as "man-woman," painted as perverts and monsters, put in literal freakshows, and forcibly institutionalized to sit by quietly while non-transmascs loudly and confidently claim that "female masculinity" has never been targeted as much as "male femininity" has. Read some trans and queer history that isn't only about gay men and trans women before you open your mouths about butches and transmascs, or better yet just listen to us about our history and experiences in the first place.

[februarys-wednesday]

starkid fans when they see Normal Man and his Barista Crush onscreen for 0.5 seconds:

[lolbree]

triple baka trio when they're called to do an interview

[parisoonic]

last ones i swear

[miguxadraws]

new buttonblossom era