this true, but in physics (and in maths too, especially in real analysis), we use differentiation as a equivalent transformation, in a generalised sense. we often come up with ways to define it with something like - finitely many discontinous points or something, which we can iron it. but major problem here (i think) is order of operation - we can not interchange sum and diff when they both depend on x

if i am not wrong, there is only one problem - sum to x (x times)

when we write it in a bit more concise but equivalent notation - d/dx sum_1^x x it basically becomes x^2 again. It is kinda a a=a proof, so not very interesting but that is the only problem. since sum is happening a variable number of times, we can not really let it loose.

in a more reasonable wording - what the image showed was interchanging differentiation and sum (like instead of doing sum after diff, instead of before), and such operations are allowed, but if the sum and diff are independent (not based on same variables).

this interchange works if you used some other variable which is independent of x

there are about 432 = 4! ways that is 24 and if it alarms after 3 tries, it can be safe-ish.

this is me confirming that this is my feddit.uk account, am confirming from lemmings.world

that explains it

I am up for moderation, will also spin up a account for moderation. I currently also moderate a few communities. Not very active, but do check twice or thrice a day

lemmings.world or pifed.social both are general purpose, and relatively small

I do this. I almost always pack extra information, and then skip according to time. In case someone questions back, I say, it was back on so and so slide, you might have missed it

a tshirt and pyjama, always

most solids and liquids are practically incompressible (when comparing with gasses). there is a relationship between bulk compressibility, shear stress and youngs modulus for solids, which can be extended for liquids. It does not work for gasses

they all are chronically ill, they will die, just in some time

you are not adding enough water, add more

i never said they did any thing wrong, and they iterated really well. They were not the smartest fellows, but they learnt to use whatever they had really well.

if we can reach it, it is done for, no ifs and buts

I would say romans iterated well.

I feel you. Not a american.

how are we quantising water shape (droplet vs jet)? Is it amount of pee generated/unit amount of time or something similar?

by a very specific definition of “inside”