mango's no.1 fan

I see pattern I draw pattern 🙂‍↕️

May would 100% be down to see the yinyang daemons, ohagi and daifuku. I absolutely love the amount of times this series has played on pairs being opposites!!

Intersex bodies do not need correcting, intersex bodies are not unnatural. Intersex people deserve autonomy.

From the second equation we get that cheeseburger plus fries-squared is five. Subtracting cheeseburger, which is six, from both sides, we get that fries-squared is negative-one. Math fans will know that there are two solutions to this; either fries are the "imaginary unit" 𝒾 or they are its negative, -𝒾. We'll do the rest of the problem with 𝒾, keeping in mind that at the end we should also take the complex conjugates as solutions.

Finally, we have that cup to the power of fries, minus cup, equals three. Replacing fries with 𝒾, and moving a cup to the other side, we get that cup-to-the-𝒾 is equal to cup-plus-three.

Now, the weird part about this is the cup-to-the-i. The problem with this is that complex exponentiation is technically not a thing. That is to say, there is no one function which is mathematically equal to "input-to-the-power-of-𝒾". In fact, there are infinitely many such functions.

Fortunately, due to reasons that take about six pages to explain (trust me I've done it), there is one particular function that many people have agreed is "the most reasonable one". This is not a mathematical notion, but a human preference. Seeing as this question was presumably written by a human, I am comfortable with using this function.

So, what function is this? Well, given a complex number r∠θ written in polar form (if you don't know what that means don't worry), where -π < θ ≤ π, then (r∠θ)^𝒾 = e^(-θ)∠ln(r).

Applying this to our problem a value r∠θ will be a possible solution for cup if e^(-θ)∠ln(r) = r∠θ + 3. Splitting this into real and imaginary parts, we get two equations: e^(-θ) cos(ln(r)) = r cos(θ) + 3 and e^(-θ) sin(ln(r)) = r sin(θ). We can graph these equations on Desmos:

let the value of the glass = z, for z ∈ ℂ:

z^(±i) = 3+z

let z = r·e^(iθ) for r,θ ∈ ℝ, -π < θ ≤ π

∴ z = r·e^i(θ+2πn) for all n ∈ ℤ

∴ (r·e^i(θ+2πn))^(±i) = 3+r·e^i(θ+2πn)

distribute powers (apologies for the use of ∓):

r^(±i)·e^(∓(θ+2πn)) = 3+r·e^i(θ+2πn)

convert to the same base:

e^i(±ln(r))·e^(∓(θ+2πn)) = 3+r·e^i(θ+2πn)

split into real and imaginary components:

re: cos(±ln(r))·e^(∓(θ+2πn)) = 3+r·cos(θ)

im: sin(±ln(r))·e^(∓(θ+2πn)) = r·sin(θ)

I will admit I REALLY like the recent improvements they've added to tumblr's search (you can exclude terms now!! you can search multiple tags!! and time frames!!) so it's not like they're incapable of adding useful features. it might be mutually beneficial for us as users if we were more vocal about things we want and don't want. Some features I'd like to see added:

spoilerable text

spoilerable images

the return of hover text!! remember when we had that?

ability to embed videos in reblogs

ANIMATED GIF ICONS!!!!!!!!!!!!

the ability to turn off other people's animated gif icons

the ability to filter original posts on a user's ENTIRE blog, not just a tag/search

more html support, like what if we could build tables

adding reactions to replies! I'm glad we can like them more but it'd be nice if we could take this further

embeddable tiktoks?? I don't even use tiktok but I remember trying to embed one in like 2020 and I'm surprised we still can't! even vines were able to be embedded

being able to search in your DMs. not being able to do this is why I tend to redirect mutuals to discord

MUTING USERS POSTS/COMMENTS WITHOUT BLOCKING THEM! just cause I don't want to see someone's posts doesn't mean I don't want us to never interact ever

a mutual-only dashboard feed

a feed for the blogs you're subscribed to

get rid of tumblr tv lmao I've literally never used it

"mark as read" button for communities without opening them

please dear god no AI shit unless it's a way for me to filter/block it easier