help-28

[valid nimbus]

wait

how will u know which of the 8 boxes

our point lies in?

[austere cove]

our boxes are sets of points

[valid nimbus]

if u didn't know where the point is in our box itself

[austere cove]

we just do a set intersection

[valid nimbus]

I see

OH I SEE

you already did the set intersection

For this big box

and found out we have a particle there

point there*

[austere cove]

exactly

[valid nimbus]

yeah cokl

cool*

[austere cove]

so we can keep shrinking our box as much as we care to

[valid nimbus]

right but, this idea kinda seems really hard

how will u do a set intersection of INFINITE points boxes

like how do u do it co ordinates wise

or give me an example

[austere cove]

we're not making, like, things you can implement in real life or anything, we're talking about abstract mathematics. We can do intersections of infinite sets because our rules of set theory say we can

[valid nimbus]

well in real life, I believe this is kinda possible, but like, even in abstract mathematics, how will you knows co ordinates of infinite sets I mean.. doing the calculations would be insanely hard (impossible) without any rule for all the calculations

I imagine that you could do something like, taking 8 points of corners of a box, and u make it into some sort of a set

and then intersect it with the outer space

and see if the point we have, is in that box

but this process really is undefined still (at least for me)

[valid nimbus]

can u give me like an actual case?

so it would be better for me to understand

[restive geyser]

Making sense of incredibly large semi-primes and all the maths that was involved with it is at least a hundred years older than the first time we'd ever used them in encryption, for an example

We didn't say "oh we don't have computers" to conclude that "oh we shouldn't study this"

[covert heath]

did hear rsa

[valid nimbus]

right so you developed a method to do this, to get positions of objects

and possibly more

hmm

I wanna know that

if I can

[knotty grail]

not sure if this is going to answer your question
but to find the x-coordinate for example you can find the perpendicular distance of the mushroom from the plane created by the y and the z axes

[valid nimbus]

I see

Hmm

[knotty grail]

something like this (red dot is the mushroom and blue plane is the y-z plane)

[valid nimbus]

Ah I see

I get it now

[knotty grail]

move along x-direction and find the distance it needs to travel to fall on the y-z plane

[valid nimbus]

Ahhh

I seee

[knotty grail]

do the same for the other two to find the y and z coordinates

[valid nimbus]

but

how would u do this

[covert heath]

distance of the mushroom cloud from the plane sounds like a very Gay problem to have

(if you dont get the joke im sorry)

-# cf. Enola Gay, the plane whose engineers actually worked on the problem in question

[wary condor]

period.

[valid nimbus]

what does "moving" along x direction even mean? I mean, I get the idea.. but are u actually doing things like "let's move 1 unit in x direction, is the point in between 0-1 ? yes then move back by half, if no, move to 2 and so on

[valid nimbus]

but how would u know?

mathematically

cause like.. in empty space it seems really absurd for us to behave like humans

[knotty grail]

because thats one way to define the coordinate of the mushroom

[valid nimbus]

hmmmmmmmmm

[knotty grail]

just like how you say that the x-coordinate of a point in a 2D plane is the perpendicular distance of the point from the y-axis

and the other way

[valid nimbus]

I see

[knotty grail]

here the x-coordinate is the perpendicular distance of the point from the y-z plane in our system

[valid nimbus]

hmm

and, you are able to do this for multiples of points right?

aka, an object like a mushroom

which has a lot of points

[covert heath]

for multiple points*

[valid nimbus]

but, how would you denote the mushroom's position

cause like u have a lot of points to say, which one r u gonna pick

[knotty grail]

in the real world in branches of science such as physics its inconvenient to mark every point of the mushroom but sure

[covert heath]

centre

[valid nimbus]

I see

[knotty grail]

in general we go with easier to process points such as the center of mass of the mushroom

[valid nimbus]

hmmm

what about

a

wait but mushroom doesn't have a centre

???

[covert heath]

guess what

you can

[valid nimbus]

huhhh

[covert heath]

say it with me

define one

[knotty grail]

its something called a centroid

although not as obvious as a square

its there

[covert heath]

well it could be anything

[knotty grail]

and its definable

[valid nimbus]

ddddefine one hmm

[covert heath]

but yes you can define one

like centre of mass

[valid nimbus]

I see

[covert heath]

(no we dont need to invoke actual mass for this)

[valid nimbus]

yea, like an example

hmmm

[covert heath]

just same formula

[valid nimbus]

that is pretty cool

[covert heath]

(mass can just be a constant mass distribution or smth)

[valid nimbus]

I'm sure u can get the formula for doing the location for a point pretty easily now

hmm

[covert heath]

...what.

[knotty grail]

any other doubts

[valid nimbus]

hmmm

[valid nimbus]

what is the formula tho?

is there a way for u to mathematically check if the point is there in your box of calculation

without knowing the position of the point at all

for humans, we can see and tell even though we can't precisely see where it is, we can see and tell where it's not pretty much

but mathematically, how would you add that in the formula itself?

[knotty grail]

hmm

this is where im confused

if you want to go into it mathematically

[valid nimbus]

yeee me too, I imagine that in computer simulations, u do algorithms that magically (seemingly) check it just like humans

but how so, mathematically

[knotty grail]

just placing a point in space wouldnt make sense if you didnt know its coordinates

[cinder thorn]

algorithms are not magical and often rely on math...

[valid nimbus]

well I need to know what algorithms and programming and coding is, in terms of atoms like... how is something like that even possible in our atomic world

but anyways

this is where I left off, for any new person willing to answer

[knotty grail]

im not sure if theres actually any formula for finding the coordinates of a point

or whether anything like that is necessary in the first place

[valid nimbus]

if measure theory exists, I think that's necessary

[jade pebble]

STILL GOING???

[astral wyvern]

whats the problem here?

[jade pebble]

HOUR 7

[jade pebble]

do not check pins

[deep gale]

pre-uni measure theory fr

[astral wyvern]

crazy

[slate glacier]

Help channels have gone for way longer before

[valid nimbus]

@astral wyvern

[valid nimbus]

I'm legit typing every single minute

[jade pebble]

thousands of messages in this

[valid nimbus]

they probably were lesser active

[jade pebble]

yes

[valid nimbus]

For example #help-25 is longer but not active

[slate glacier]

True, they were really tough problems for help channels

[valid nimbus]

We are here right now

if anyone wants to answer this

[slate glacier]

What's exactly the question?

[valid nimbus]

so

We came to the construction of OABC

the basis vectors

and then, we're on our task to find the co ordinates of a random point

that we don't know

[valid nimbus]

Now u can read that ^

[slate glacier]

Alright I see

[knotty grail]

i suggested he take the perpendicular distance from either of the three planes to find the coordinate values but OP wanted it in a formula(?)

[slate glacier]

Yeah TBH finding the perpendicular distance from two sides should verify whether it is in the field or not

[covert heath]

its back to gibberish

[valid nimbus]

but

how do u "verify" it

with maths

?

[slate glacier]

Okay first of all let me confirm, you've got four Vectors that make a parallelogram correct? They have some area they contain inside?

[valid nimbus]

No

OABC is not a parralelogram

O is the centre

oa, ob, oc

is basis vectors

x, y and z axis

[slate glacier]

Ahhh, like a 3D coordinate plane

[valid nimbus]

Ye

[slate glacier]

So wait, and you want to know how we figure out where a point is relative to that?

[cinder thorn]

how would you "check if your point is in your box of calculations", i.e. check its position, without "knowing its position"? it's self contradictory, as I understand it

[valid nimbus]

yeah..

that's what I'm asking

how do u check the position

[slate glacier]

Yes exactly

[valid nimbus]

with a mathematical formula

if u can't, then how do u model the position at all

[slate glacier]

Well you must know something about it to start

[cinder thorn]

you're asking different things

[valid nimbus]

I'm sure measure theory has an answer

[deep gale]

Linear combination of basis vectors provided there is a sufficient algebraic structure

[valid nimbus]

but I'm just waiting for someone to tell it

[valid nimbus]

yeah there is

but how would you use that algebraic structure to determine the position of this random point

[deep gale]

linear combination?

[valid nimbus]

linear combination? as in?

[deep gale]

adding homotheties of the basis vectors

[valid nimbus]

hmm

what are homotheties

[deep gale]

if you dont know, you dont know, if these vectors are indeed basis, these homotheties will exist for each vector in the space but you may not know their values

In general these homotheties need not even be complex numbers

[cinder thorn]

like the point $M(5, 2, 1)$ is the point such that $\vec{OM} = 5 \vec{OA} + 2 \vec{OB} + \vec{OC}$

[glossy valve]

bloubbloub

[deep gale]

They could be abstract in a field that's not isomorphic to real numbers

[cinder thorn]

let's not overcomplicate this for him

[valid nimbus]

oh so the co efficients

pretty much

[cinder thorn]

that's what coordinates are yes

[valid nimbus]

right, you don't know their values, but for u to know the value, how would you do this?

back to the question; you have a random point, how would you find it's co ordinates

the "homotheties" indirectly. how would you find them

[deep gale]

Plz tell me this is not related to quantam/particle physics

[cinder thorn]

no

[valid nimbus]

it's not, I'm asking it in 3 dimensional space lol

a mathematical 3 dimensional space

[deep gale]

What does random mean tho

[cinder thorn]

in an euclidean space (probably what you are thinking about) you can do the dot product with respect to each basis vector

[valid nimbus]

random doesn't mean something like an orbital cloud here okay?

[covert heath]

not again

[valid nimbus]

LOLLL

[valid nimbus]

random just means that, we don't know it's position

and someone has given it's position

don't take it too literally

[valid nimbus]

And we need to find that

like they didn't give it to us

they kept the point at a position and we need to find that position

[deep gale]

Well if you want to do math it's not necessary, but would be nice to do it the basic universal way, that is have precise axioms and definitions, so i would advice to define "random" precisely

[cinder thorn]

please I beg you to stop using ambiguous terminology

[valid nimbus]

Alright yeah

[valid nimbus]

alright lol...

[cinder thorn]

good

let's say you are in 3D euclidean space. The way you find the coordinates of a point with respect to an orthogonal basis is by taking the dot product

with each vector

[valid nimbus]

that requires for you to already know the co efficient or homotheties

what if you don't know those

[deep gale]

Why can't you just write it as a linear combination with unknowns then? If you don't have information , then you don't , thus you can't do what you want, but you can instead write it as a linear combination with unknowns and you can even do the dot product projections or whatever too

[cinder thorn]

You need to know its coordinates in some basis at some point

otherwise what do you know about it?

[valid nimbus]

nothing

but

isn't measure theory's purpose is to study stuff like this?

[deep gale]

If you introduced a more interesting notion of randomness, things could be different

[valid nimbus]

Hmm

[cinder thorn]

no

when we mentioned measure theory it was when you were talking about "infinitely small width" or somth

[valid nimbus]

well then, does every model of a mathematical universe have only 2 or 1 points so we could keep 1 point as the origin and the other as any one of the basis vectors?

do we not have many points, distances and etc..?

[valid nimbus]

I see

so every distance is essentially "x units of its own?", is a 3 pointed universe not possible?

[valid nimbus]

I mean... it is possible if

u define a third point

on your own

but to find the third point

when u don't know where it is

but if u don't find it, u won't know the distance

so is the distance not possible with an unknown third/more point(s)?

[cinder thorn]

let's me clarify something: any model of the universe is not made by math but by physics

anyways

[valid nimbus]

I don't mean our universe but yeah go on

[deep gale]

applied math

[deep gale]

thing is

Vectors and vector spaces

Aren't really space-like entities

They are algebraic in nature

[cinder thorn]

so what's a mathematical universe ?

[valid nimbus]

Hmm

[deep gale]

Well unless if

[valid nimbus]

I can see why vectors are like that

but POINTS

are not like that

they're objects

[deep gale]

We're talking about vector field stuff , but that's kinda in the definition so whatever

[valid nimbus]

space in nature

right?

[deep gale]

Mathematically a point like say (1,0,0)

Is just an element of a cartesian product set WHICH is actually kinda tricky to define precisely

Like

Cartesian product isn't hard to define*

A pair is a little more tricky to define is what i mean

[valid nimbus]

a pair?

hm

[valid nimbus]

why so

why can't u define it precisely

1,0,0 isn't it truly precise?

[cinder thorn]

that's besides the point

[deep gale]

Well you would have to define it as a set , but the question is what set exactly?

[valid nimbus]

Ah

[valid nimbus]

the set of all possible points in a 3 dimensional space?

[deep gale]

Kuratowski/wiener definitions is one example

[deep gale]

No like

Set theoretically

[valid nimbus]

yeah give me an example

a simple one

by what u mean

[deep gale]

https://en.wikipedia.org/wiki/Ordered_pair#Kuratowski's_definition

[covert heath]

goddamnit we're now on set theory

[valid nimbus]

ordered pair? is a pair of objects in which their order is significant?
hmmm so b, a and a, b makes a difference now?

so the set of rooms through which a human has to walk

for example; room of air with concrete floor, room of water with marble floor, and room of fire with thorns

u change the order, the human would die in the first room

is this what u mean?

or give me an example of a ordered pair

[covert heath]

coordinates are ordered pairs.

[deep gale]

Cuz set theoretically {a,b} = {b,a} is indistuingishable like that bcuz roughly speaking sets are equal whenever they consist of the same elements , ordered pairs demand you distinguish

[covert heath]

(2,3) is famously not the same as (3,2)

[valid nimbus]

I see

but

[deep gale]

But {2,3} as a set is the same as {3,2}

[valid nimbus]

2,3 is not a set of points tho

it's ONE point

[covert heath]

its a set of numbers

[queen flame]

How long has it been

[covert heath]

https://tenor.com/view/its-been84years-titanic-rose-dawson-gif-5372593

[valid nimbus]

I don't understand the reason for you to specify numbers here soo immaterialistically

so what if it's a set of numbers?

[covert heath]

what

[valid nimbus]

So what if 2,3 is not the same of 3,2

?

I gave u 2,3 and not 3,2

[deep gale]

Did you learn about basic set theory before?

[covert heath]

theyre in 9th grade

[valid nimbus]

yes

[valid nimbus]

so what is your problem here? are you just saying " Hey, I know we're kinda unrelated to your 3 dimensional space , but just so u know, if you wanna go to 2,3 co ordinates, here's a hint: don't go to 3,2 instead"

[valid nimbus]

and, if I want to define all the points inside a 3 dimensional space as a set

I don't see how this is coming in front of my face saying "hey changing the order means different! I'm a problem in your face now"

why can't I include 2,3 and 3,2 seperately?

[valid nimbus]

is there a fundamental law in your set theory that says "hey those kinda look the same because I'm blind, so u can't include both of them"

@deep gale

[cinder thorn]

the 3d space you are talking about is the set of all ordered sets (I mean pairs but with 3 numbers) of 3 real numbers

[valid nimbus]

yes

so what is the problem

[cinder thorn]

theres no problem

[valid nimbus]

in me giving all the combination of those numbers

so? I can give 2,3,0 and 0,3,2

and

where's the problem of "rigorously defining things" here

which they said was

[valid nimbus]

here

[valid nimbus]

tricky to define precisely

[deep gale]

well if you insist on doing math like this anyway, perhaps looking into some yummy basic formal math wouldn't be much of a problem.

[cinder thorn]

it's not related to your original question

but I would still advise you to read it if you have the time

[valid nimbus]

well technically if u have a different direction of x, y axis

2,3 would be the same as a different axis' direction's 3,2

[deep gale]

but as sets {2,3} and {3,2} would be equal

[valid nimbus]

you're missing something over here that makes u think they're tricky

as sets with defined, limited elements

aka one element

those both co ordinates, are points

all 0 dimensional points are equal

therefore they would be equal and they aren't affected by position at all

but

if we're talking about all the possible points, with a condition

say " x | x, y, z axis are situated in so and so directions"

and u have another set

x | x, z, y are situated in so and so directions, different than set 1's order

these both would not have the same elements

even though they would

[deep gale]

well not really tricky , but if you have that a is not equal to b and end up defining (a,b) = {{a},{a,b}} now you can talk about (a,b) not being equal to (b,a) , because the set {{b},{a,b}} is different from the set {{a},{a,b}} because the element {a} is not equal to {b} , because as sets they are not equal to

[valid nimbus]

I mean* they won't be equal

even though their elements would be same

It's kinda wrong to define this with set theory

because a point in one world

would exist in the other world

set*

but it would be different co ordinates

you would have, for example, 3,3 in set 1 equaling to 5,6 in set two

[valid nimbus]

does that mean 3 = 5 and 6 = 3?

[deep gale]

and now you can do this and even do R^3 = RxRxR which is actually the definition

[valid nimbus]

no

[deep gale]

the construction (a,b) = {{a},{a,b}} does satisfy the ordered property with x = x' and y = y'

[valid nimbus]

you said " Because the element a is not equal to b, because as sets they are not equal to"

something just troubles me here

If u take element a, with x, y and z axis pointed towards a specific arbitary direction (situated as one) forming the set a lies in

[deep gale]

it actually isn't , because it gives you a construction , if you were to strip the euclidean space out of it's special algebraic,geometric,topological etc properties then you would get just a cartesian product set

[valid nimbus]

and if u take element b of a different set, that is formed by x, y and z being situated in a different position

[valid nimbus]

then even though, a does not match with be (how 3 ≠ 5)

a would be = b

because if you intersect them into one world, or perhaps remove the point of both a and b after merging them into one world

you would find that a was in the same place as b

so a = b even though as numbers they differ

how does your set theory talk about this?

[deep gale]

how does that form a set?

[valid nimbus]

x axis is situated vertically, y axis is situated horizontally, and z axis kinda both if u get it

the set is

all possible points

x | x axis is situated vertically, y axis is situated horizontally, and z axis kinda both if u get it

[deep gale]

sure but what is a point?

[valid nimbus]

a point is a 0 dimensional object that is situated in any arbitrary co ordinates x, y, z (exactly as such without the object needing more co ordinates)

[deep gale]

what's a 0 dimensional object

[valid nimbus]

if u wanna talk about it in set language, u can

[deep gale]

no, that depends

[deep gale]

The primordial structure of a large portion of mathematics lies in sets.

[valid nimbus]

a zero dimensional point x, is such that;if the set of all co ordinates of x taken as A, and situated in a euclidean 3D pace, then the set of any ONE location's co ordinates that makes up the location of x as set B.
Then set B - Set A would be the empty set, indirectly pointing that any x, y, z is a point.

[deep gale]

That definition is circular tho

Because i asked you waht a point is

[valid nimbus]

yeah how about now

[deep gale]

You said point is a 0 dimensional object that is situated in any arbitrary co ordinates x,y,z

[valid nimbus]

I removed the point

all co ordinates that intersect with object x

which, u and I both know is one.

[deep gale]

what are co ordinates tho

[valid nimbus]

co ordinate is any arbitrary combination of x, y, z for 3 dimensions, x1, y2, qn for n dimensions

[deep gale]

What's an arbitrary combination? Also what is x,y,z and what is a dimension?

[valid nimbus]

any possible combination of real numbers is an arbitary combination

so x1 can be any real number

[deep gale]

now we're talking slightly more concrete

but there is a problem

[covert heath]

still going??

[queen flame]

Bro gained active in 2 days

[covert heath]

in one day

[valid nimbus]

12 hours

[queen flame]

oh

[deep gale]

real numbers are also defined in terms of sets when you strip away almost all of their structure too is one thing, but the main problem is that you still didn't define what a combination is

[covert heath]

hooboy

time to plug another roof

[deep gale]

nyehehe

[valid nimbus]

x, y, z is an arbitrary combination of real numbers in each x, y and z such that (x,y, z)'s complement - x, y, z ≠ the empty set

[covert heath]

time for AllTheNumbers™

[deep gale]

bro maybe we should take a tea break or something lel

[covert heath]

https://www.youtube.com/watch?v=dKtsjQtigag&t=2335s

start here

[valid nimbus]

a combination, is any possible real number possibility of the variables x, y, z

x should be any real number, y should be any real number, z should be any real number

at the same time

then it would be called as a co ordinate

[valid nimbus]

maybe lol

I'm not used to set theory language

I have to think every word through, to answer u rigorously

[covert heath]

watch another roof.

thats homework

[austere cove]

I'm back, sorry for the disappearance

are we talking about ordered pairs and set theory now?

[covert heath]

Apparently, yes.

[civic bay]

no way this is still going 😭

[valid nimbus]

hii

we left off at how to find the position of a partic- point*

no one's answered that yet

[austere cove]

well, I gave you the beginning of a procedure right?

[covert heath]

holy shit we still dont know how coordinates work?

[valid nimbus]

yeah but the procedure didn't make sense

[valid nimbus]

can u read this and especially the last sentence

[valid nimbus]

I mean.. it did make sense

actually

[austere cove]

well, can you explain to me your understanding of the procedure, and why you think it doesn't make sense then?

[valid nimbus]

Well, you said me we can make a box around the point

if you don't know the point's position

how do u know the box is containing that point?

You said that u can use intersection to find out, but how?

[austere cove]

we don't, choose two points at random from the bag, and use this at the bounds of your box.

check if the point is in that box

[valid nimbus]

Ah from the bag

[austere cove]

repeat until it is

[valid nimbus]

but how do u check this

[austere cove]

set intersection

[valid nimbus]

And how do you get an actual computable answer

?

[austere cove]

You're not going to like the answer.

for the vast, vast majority of points, there is no computable answer.

most points cannot be expressed with a finite amount of data.

[valid nimbus]

oh

...

[austere cove]

look up computable reals.

https://en.wikipedia.org/wiki/Computable_number

[valid nimbus]

I see

[valid nimbus]

How about something more simple

We categories the world in whole numbered boxes

You have to find one of those

Each box has 1 coordinate, integers

X,y, z

How about now

[austere cove]

Now you can test each point one by one until you find it

[valid nimbus]

... and this was your answer

this... was the mathematical idea

[austere cove]

what I'm saying is, now, in principle, this is possible.

and because it's a finite point, it will always be a procedure that ends, if we check the points in a valid order that will list them all.

(This is the difference between a countable and uncountable infinity)

(And this is why I've been careful to say "bag" instead of "list" in certain cases)

[valid nimbus]

Hmm

[austere cove]

you can obviously come up with smart procedures to check the values more rapidly

but essentially that's all that is needed

[valid nimbus]

well, that's just saying "If you had a lot of years, you would be able to finish a lot of bread" within giving a formula or a method to finish it the best...

[austere cove]

math isn't always concerned with the fastest implementation

[valid nimbus]

I see

[austere cove]

just whether or not the implementation is possible.

[valid nimbus]

well....

so even in mathematical worlds

Positions and(of) points are insanely impossibly

[valid nimbus]

something that concerns me is that

if knowing all the points (depicting them) is really impossible with finite data

[austere cove]

in set theory, we define real numbers by considering the set of all rational numbers less than or equal to it.

[valid nimbus]

then how does measure theory, measure distances and others

that are so abstract and require 100% precision

which is really impossible because half the time, you can't even count or note down all the points in between

to get the line

[covert heath]

do you think theres an international standard list of numbers somewhere or smth

[valid nimbus]

well, I just thought depicting any point would've been possible

but looks like most of it isn't

[valid nimbus]

in terms of co ordinates

[covert heath]

...huh?

[valid nimbus]

@austere cove my next question is this; how does measure theory measure the distance. I mean sure, u can say oa is 1 unit and that's the distance between o to a, but how would relate that unit to something like cd? comparing it is sheerly impossible right?

[valid nimbus]

depicting every point*

would've been possible

[cinder thorn]

this is not measure theory again

[valid nimbus]

but guess it isn't

Isn't distance measure theory

[austere cove]

it is possible, it just requires an infinite amount of information

that you need to gather from the point

[cinder thorn]

not really

[austere cove]

and the way to gather that information is through the box procedure or another similar one

[valid nimbus]

well something that concerns me more now is

how do u know if one of the 8 points that u took

is the point that I took

or I situated

how do u know the 8 possible places of a point

has an actual point that i placed

[austere cove]

if I somehow guess your point in the interior of the box, which is not impossible, then it will be within all 8 of the boxes.

[valid nimbus]

how does math convey a point exists somewhere

[valid nimbus]

no if each of those boxes can contain only 1 point

[austere cove]

???

[valid nimbus]

if the boxes themselves are 0 dimensional

but

i placed a point somewhere

how do u check if the point exists in your boxes or not?

[austere cove]

here's the thing about real numbers, they are infinitely stretchable and shrinkable, each segments of the real numbers contain exactly as many numbers as any other segment and as the whole.

so each smaller box has the same number of points as any other

[covert heath]

^^

[valid nimbus]

I don't mean it in that way

let's talk about

the integer /whole number boxes now

u have 8 boxes okay?

[austere cove]

you don't need the boxes for the integer thing

[valid nimbus]

how do u check if one of those whole number boxes, contains my whole number co ordinate point

[austere cove]

you just need to list them off.

[covert heath]

why does bro put a slash between two things that are not the same

[valid nimbus]

no I mean..

[covert heath]

integers arent whole numbers

[valid nimbus]

if u say 55,66,22

then how do u know that co ordinate does not have the point

that I put

?

[austere cove]

I'm sorry, I'm not sure what you mean here.

[valid nimbus]

mathematically

[valid nimbus]

like

you said

I need to list off the co ordinate, I don't need boxes, till I find the point (which I had no information about)

[valid nimbus]

and to find this point, if I do a process of taking all co ordinates, if those co ordinates were whole numbers from 1 to 100 for example (x /y /z can be anything from 1 to 100 )

[austere cove]

Here's a procedure for listing off coordinates in 3d, first list the origin. Next, list all coordinates whose magnitudes total 1, i.e. (1, 0, 0), (0, -1, 0), etc. then all with total magnitude of 2 such as (-1, 0, 1), or (2, 0, 0), then 3, and so on

[valid nimbus]

Then how do I check if there's a point in any of those boxes? like if I get box 55

how do I check if there's a point in it

I didn't have any information of the point

so even if I have finite boxes, say just 100 boxes for our sake

how do I even check which box has a point, to locate the point

[austere cove]

I thought you said this point had integer coordinates, yes?

[valid nimbus]

Yes

[austere cove]

then you just test that your point is the same as the point in your list

[valid nimbus]

how?

how do I do the "testing"

[austere cove]

how do you test any two sets for equality?

[valid nimbus]

intersect and check if something is left?

[austere cove]

intersect and check if everything is left.

[valid nimbus]

yeah

but

if u dont know anything about this point

[austere cove]

so?

your coordinate and the actual representation of the point as a set are different things

[valid nimbus]

then how do u expect to do an intersection and get an answer other than " Hey we found nothing that's out of the ordinary like a point"

u dont know if the point exists

[cinder thorn]

it's like asking "how can you see the invisible man if you can't see him"

[valid nimbus]

yeah

how can u detect this particle, if the mathematical operation that you're doing

[cinder thorn]

and what do you expect us to answer

[valid nimbus]

called intersection

does not detect this point

how do u know if it detects the particle?

how can maths already know something, and when ur computing it, how do u expect it to give the answer

it's like you're talking to a magical paper

that gives u an answer that u ask

u have to do the computation

u have to give the inputs

and if u dont know anything about the point

u wouldn't input anything like a point in one room

and u just calculate whatever u know, u intersect 2 rooms and see if everything is left

[cinder thorn]

the point has coordinates even if you don't know them. you can still apply a function (say a distance function) and get an answer

[valid nimbus]

and u wouldn't find the point

[valid nimbus]

yes but how will u get the answer if you didn't input the point

does maths already know

okay wait

let me give u a bit more

[cinder thorn]

maths is not someone so it doesn't "know"

[valid nimbus]

understandable idea here

[valid nimbus]

when I'm computing a path integral for my spaceship

maths does not know if there's a rock coming in the way

it's calculated on the stuff I give it

okay?

[austere cove]

path integral? a path integral of field?

[valid nimbus]

now here, I don't give it a point because I don't know it

[cinder thorn]

please be preciseee

[valid nimbus]

no like the path integral from gravity

[austere cove]

you just mean your trajectory?

[valid nimbus]

8 planets and the suns gravity, where would the spaceship move

[valid nimbus]

yeah sorry for the

mis disturbance

[austere cove]

because a path integral is something specific

[valid nimbus]

right

alright so

this trajectory

if a rock comes in between

it will break

but maths only did everything according to what it was given

[austere cove]

you're asking, how do we know whether or not there are points that we did not define?

[valid nimbus]

over here we don't give it the point, just like how we don't give it the rock

[valid nimbus]

no

how do we know that the set contains the point or not

and

if we don't know what the set contains

how can we run a meaningful intersection

and expect the answer to be true

where will we form this?

[austere cove]

we defined our 3 dimensional space to have regularity

that regularity is encoded in the metric

[valid nimbus]

yes, and I don't argue anything irregular

I'm just saying

if I have to calculate two sets' intersection

I need to know what those two sets contain

to get the answer meaningfully

but here I don't know if the point is there or not

so I can't run a meaningful intersection FOR the point

[austere cove]

a point is where or not?

[valid nimbus]

no even if the point exists in one of the boxes

how will I know

which box the point is

[austere cove]

we can simply test your point against the definition of the box.

[valid nimbus]

how will maths know this when it's doing the intersection of those two boxes

[austere cove]

your box is defined as "all the points in the region that satisfy these criteria"

[valid nimbus]

because maths is done on what u give it

[austere cove]

then we check if your point satisfies those criteria

[valid nimbus]

no no I think you're confused here

we have empty space

and only one point

in any of those 100 boxes

[austere cove]

yes, and we make the boxes.

[valid nimbus]

boxes are imaginary co ordinates of space

now

the point should exist in any one of those

but

This is like saying

Check if 5x - 5y = c

you don't know what x and y are

[valid nimbus]

because

you don't know if a point is in those two boxes

so when u do the operation (of interscting them sets, on your paper using a pen)

you will not get an answer that contains a point

because you didn't include that point

in your set

it's mathematically impossible for it to come

only if u ask the person who put that point

he will give u a correct answer

but when u don't know anything about the point

u meaningfully can't do anything that checks if the point exists anywhere

u sure can " See" but that's human and not... mathematical

[austere cove]

If you know absolutely nothing about the point in question, then it is impossible to locate a point in a coordinate system. You need information about the point.

[valid nimbus]

yep

that's what I'm saying

and now I'm asking you

[austere cove]

I gave you a procedure that you can use if you only know how to test whether or not that point is in a particular set of points.

[valid nimbus]

what information do u need?

[austere cove]

which is pretty much the smallest amount of information you can possibly know about a point

[valid nimbus]

not exactly

to know if the point is 0 dimensional or 1 dimensional

[austere cove]

all points are 0 dimensional

[valid nimbus]

well, if it's two points

[austere cove]

then it's not 1 point

[valid nimbus]

or one point

alright

if it's a

[restive geyser]

And this has been pointed out to you at least a dozen times

[valid nimbus]

if it's a point that came when it was 3000 bce for humans, or whether if it's a point that formed at 2025 bc for humans

this is lesser information

than to be able to "check" If a point is there in a box

[valid nimbus]

that's I think, the most information u can get

[restive geyser]

-# the opposite of BCE is CE; BC means BCE already

[austere cove]

@valid nimbus I applaud you for your persistence. But I think I'm going to stop here, and I am becoming less and less certain that you are acting in good faith. I wish you the best.

[valid nimbus]

hmm, alright

I'll be closing this thread now too

[cinder thorn]

lol

[valid nimbus]

it's been 13 hours and 40 minutes

I did get a lot of meanignful information

[cinder thorn]

really

[valid nimbus]

yes but we're all at stage 0s of our own right.. a president doesn't know which decision to take, a child doesn't know which ice cream to pick

well anyways, thank y'all

[cinder thorn]

one last note : you seem to think that with math you can only do calculations by giving all the info beforehand. But in this case you can imagine that we have defined objects before defining their properties, and not the other way around.

[slate glacier]

Looks like I got here just in time lol (in terms of witnessing the closing of this channel)

[deep notch]

we can help me now

[slate glacier]

you can get a separate channel mate

[austere cove]

he already has one

[restive geyser]

Keep asking like that and no one will

(He has one)

[valid nimbus]

alright

[slate glacier]

Ahhh I see

[valid nimbus]

good bye everyone

was a fun time with you

[cinder thorn]

bye

[slate glacier]

🫡

[valid nimbus]

.close

[full forum]

Channel closed

Closed by @valid nimbus

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

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• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
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• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[earnest wyvern]

first i split it

but im not sure about the ranges

[quartz flare]

Oh that's an interesting question

[earnest wyvern]

why do entrance exams have to be like this

[quartz flare]

We want to know when $\floor{2^x}$ changes value

[glossy valve]

Coolempire93

[earnest wyvern]

oh

what do i have to really consider for these questions ive been struggling

for the floor and ceiling functions

[quartz flare]

I would think about it like

[earnest wyvern]

something to do with either the x value range or the y

[quartz flare]

Okay the lower bound is 0

[earnest wyvern]

yep

[quartz flare]

2^0 is 1

So let's see 2^what = 2?

[earnest wyvern]

so i think 0< equal to x < 1 is fine

[quartz flare]

Right

[earnest wyvern]

its just 1 < [2^x] < 2

i get that

[quartz flare]

So from 0 to 1, $\floor{2^x} = 1$

[glossy valve]

Coolempire93

[earnest wyvern]

but then i did 1 < equal to x < to 2

[earnest wyvern]

yes exactly

1 is not inclusive ofc

but yeah

[earnest wyvern]

this is the mistake and idk why

[quartz flare]

So 2^what = 3?

[earnest wyvern]

why does it have to be like that

why cant i just jump straight to 2^2 = 4

[quartz flare]

Because 3 is the next value the floor function could take

[earnest wyvern]

😭

its just log base 2. 3

how do i make that image

[quartz flare]

Compare, 2^1.5 = 2.8 and 2^1.7 = 3.249

[quartz flare]

Exactly

[earnest wyvern]

well without a calculator

uh

im not sure

[quartz flare]

They permit exact values in the answer choices

[earnest wyvern]

i cant use a calculator though

which is a problem

kind of

but i guess for [2^x] = 3 is just log 2 3

so what is that another range

[quartz flare]

We have our reasoning to know that log2(3) is between 1 and 2, so we can now rewrite the integral easily

[earnest wyvern]

so we have 0< x < 1 and 1 < x < log2 (3) and log 2 (3) < x < 2 ?

something like that

[quartz flare]

So we get $\int_0^2\left(\floor{2^x} - 2^\floor{x}\right)dx = \int_0^1(1 - 2^0)dx + \int_1^{\log_2(3)}(2 - 2^1)dx + \int_{\log_2(3)}^2(3 - 2^1)dx$

[quartz flare]

Yep

[earnest wyvern]

ah

[rotund pebble]

you have K=<E(x)<K+1 E(x) is floor function

[earnest wyvern]

but of course i gotta split the integral

[quartz flare]

Yep, as I did

[earnest wyvern]

ah

[rotund pebble]

so it's the sum if integrals from k to K+1 no ?

[earnest wyvern]

and once you put the values in

it makes more sense to draw it but i see it

[glossy valve]

Coolempire93
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[quartz flare]

Definitely

[earnest wyvern]

i hate these questions omds

i kind of get it

[quartz flare]

Understandably

[earnest wyvern]

yeah it makes sense

a bit annoying its not taught at school but oh well

where can i find more of these

[rotund pebble]

mit integration bee

[earnest wyvern]

what.

[quartz flare]

https://www.mymathscloud.com might have something on the entrance exam you are looking for

[quartz flare]

Those might be too difficult

But yes

That's a good option for integration

[earnest wyvern]

i dont think i can do mit bee 😭 do a levels even teach all of that not really

[rotund pebble]

https://www.youtube.com/watch?v=3RPC-NaVXwk&t

this video will help you

[earnest wyvern]

this is a bit too complicated

they wont ask this

[rotund pebble]

it's not thaaaat complicated this guy explains well

[quartz flare]

Well then you have mymathscloud in any case

[earnest wyvern]

nah i checked htey dont got it

[rotund pebble]

wait he made an easier one lemme find it

[earnest wyvern]

its only high school content mostly

wait hold on theres another one i wanted to show

1 sec

[quartz flare]

Very not true 😆 scroll under the course finder at the top

[quartz flare]

Well I should say

very true in that it's mostly that

Very not true that they don't have uni

I often grab textbooks from off there

For senior level math classes

[earnest wyvern]

ah

is the floor and ceiling function a uni topic or something

i havent been taught this at all

[quartz flare]

https://www.mymathscloud.com/modules/university uni page if interested

[whole lily]

Sub sqrt(x)

[quartz flare]

It's often overlooked in high school level

[whole lily]

Then convert into a summation

[rotund pebble]

we did this at 11th grade

[earnest wyvern]

i aint american broski

we dont got this

its more basic

[rotund pebble]

same

[earnest wyvern]

where u from

[rotund pebble]

but it's better to do harder questions

[earnest wyvern]

so what are the boundaries here

[earnest wyvern]

very true just where 😭

[rotund pebble]

to make it easy for you later on

[quartz flare]

We just have to think about it again

When we move from one value to the next

[rotund pebble]

there's a lot of videos on youtube

[earnest wyvern]

il do that

[earnest wyvern]

yeah im thinking hmm

[quartz flare]

Starting with flooring to 0 (i.e. sqrt < 1)

What x values give sqrt < 1

[earnest wyvern]

1

[quartz flare]

Right

[earnest wyvern]

wait

im assuming you go from 1 to 2 then 2 to 3

[quartz flare]

So integral from 0 to 1 of 0 dx is our first integral

[earnest wyvern]

so like square root of 1 and square root of 2

what would that round to and stuff

[quartz flare]

Well no not quite

[earnest wyvern]

yeah i see

[quartz flare]

We do't get 50 integrals

[earnest wyvern]

i was thinking 25 integrals

[quartz flare]

Now we need to know when sqrt floors to 1

When is sqrt < 2

[earnest wyvern]

nevermind

[quartz flare]

Less than that as well

[earnest wyvern]

ah

ohhh

what floors to one i see

so it would 0 < x < 1

and 1 < x sqrt 3

[quartz flare]

Not quite sqrt(3)

[earnest wyvern]

wouldnt sqrt 3 go to 1

[whole lily]

You don't need to do that

[quartz flare]

sqrt 3 goes to 1

[whole lily]

You can save yourself the trouble of thinking about it by substituting in sqrt(x)

[quartz flare]

But sqrt(4) is the lowest value that doesn't go to 1

[earnest wyvern]

oh.

[whole lily]

Then the bounds are just integer values

[quartz flare]

I guess so actually

They will be integer here as wel thoug

Just as a note

[earnest wyvern]

hmm

[whole lily]

Except for the last one yes

[quartz flare]

Oh yeah true

Why wouldn't they do it to 49

[earnest wyvern]

so we would go from 0 < x < 1 1< x sqrt 4

[quartz flare]

Nastyheads

[earnest wyvern]

😭

[quartz flare]

right sqrt4 being 2

You may see the pattern

[earnest wyvern]

and then sqrt 4 < to sqrt 9

yeah

[somber violet]

no, not at all

it is just one of those things you pick up and makes for nice problems which dont require difficult math

[quartz flare]

Yep

[whole lily]

\begin{align*}
I = \int_{0}^{50}\operatorname{floor}\left(\sqrt{x}\right)\dd x
\underset{\sqrt{x} \to x}{=} \int_{0}^{\sqrt{50}}2x\operatorname{floor}\left(x\right)\dd x \
&= \sum_{k=0}^{6}\int_{k}^{k+1}2xkdx+\int_{7}^{\sqrt{50}}2x\cdot7 , \dd x
\end{align*}

[earnest wyvern]

and then

im assuming the difference in x values would be the same

for most ranges

except for 49-50

[glossy valve]

Roy

[quartz flare]

Yep

[whole lily]

ok idk what's wrong with my latex

[earnest wyvern]

i kind of get the theory but writing it out is horror

[whole lily]

but then you just integrate normally

treat k like a constant with respect to the integral

[quartz flare]

Haha only 8 integrals but yeah

[whole lily]

and evaluate the resultant series

[earnest wyvern]

so the difference in x is basically 1

wait no

its 1 for the first one

3 for the next

and it increases by 2

1, 3 , 5

[quartz flare]

Definition of a parabola haha yep (sum of odd integers below 2n = n^2)

[earnest wyvern]

but the y values would increase by 1 kinda

[quartz flare]

Or something of that sort

[earnest wyvern]

ah

[quartz flare]

Exactly

The floor function at work!

[earnest wyvern]

its hard to write out

how will i draw this

6, 15, 28

[quartz flare]

\begin{multline}
\int_0^{50}\floor{\sqrt{x}}dx = \int_0^10dx + \int_1^41dx + \int_4^92dx + \int_9^{16}3dx + \int_{16}^{25}4dx + \int_{25}^{36}5dx + \int_{36}^{49}6dx + \int_{49}^{50}7dx
\end{multline}

[glossy valve]

Coolempire93

[earnest wyvern]

yk for the limits 4 and 1

wouldnt it be 2

i meant

between 1 and 4

wouldnt the area be 6

[quartz flare]

Let me show the graph

This will be helpful

[earnest wyvern]

nvm you're right

[quartz flare]

Should have done it at the beginning

[earnest wyvern]

it rounds down

i included the value of 4 for the domain

its 1 i see

[earnest wyvern]

ah

i get this right

but how am i gonna do this multiple times

i dont wanna draw the graph a ton

ohh

its a sequence

[quartz flare]

Yeah you could treat it as one

[earnest wyvern]

its like 190 + something

i cant do 49 - 50

or can i

[quartz flare]

Check my integrals for that

Or look at the graph

[earnest wyvern]

i got 197

something like that

nvm

210

[earnest wyvern]

i did

and the one i drew

OH ITS 210

i got it

yess

[quartz flare]

Yay!

[earnest wyvern]

one problem

i aint doing this in 5 minutes 😭

[quartz flare]

We just did it in like 10

[earnest wyvern]

5 minutes per question is a bit too harsh

[quartz flare]

If you get familiar with it you can do it in 5 😄

[earnest wyvern]

if i could find more questions yeahh

thanks for your help though

🔥

[quartz flare]

No problem! If you do find more (or end up asking the AI to create some) you can always ask about them here (or ask us to check your answer, don't trust that the AI answer will be correct if you're doesn't match it)

!done

[full forum]

If you are done with this channel, please mark your problem as solved by typing .close

[earnest wyvern]

got it thanks

.close

[full forum]

Channel closed

Closed by @earnest wyvern

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[little steppe]

Code question: I have a data report-style table that looks like this. The data repeats itself a billion times for month-by-month data. I want to turn this into a pivot table (so I can easily analyze month-by-month or year-by-year data), but can't easily run a pivot.

[little steppe]

(I can use Python and R and could try to finagle one of those, but wasn't sure if there was an obvious thing I was missing)

[plush egret]

pivot table means excel right?

python or R will do better

[little steppe]

excel, python, R are all fine... i want something that looks like

Type of Action | 2017 | 2018 | 2019 | 2020 (etc)...
action type A  | 10   | 30   | 15   | 5
action type B  | (data)

csv, excel, python, r, etc are all fine but i

'm not sure how to deal with the repeating headers

[plush egret]

i mean to me I'd use whatever youre comfortable with and can handle it

people say not to use chatgpt but

you can quickly confirm if it understands what your asking it to do

[little steppe]

ye i might do that

or try some really bad python

[plush egret]

i dont remember enough R to help but using chatgpt seems low-risk here

[little steppe]

lemme try it

[quartz flare]

Yeah this looks like the output from a pandas dataframe in python if you go that rout

The code would be something like

import pandas as pd

df = pd.read_excel('file_name.xls')
df.print()

[little steppe]

sure, but i won't be able to roll it up in a meaningful capacity because groupby doesn't have meaningful cols to aggregate by

[plush egret]

how are you planning on aggregating

does it go 2017 1 2018 1 2019 1

[quartz flare]

Ooo

[little steppe]

i'm going to turn the columns into years

[quartz flare]

I thought the columns were already the years

[plush egret]

you mean sum along the years to flatten all rows into a single stat?

[little steppe]

basically

[quartz flare]

Ah

[plush egret]

not that you need to clarify to us what you mean just curious

[little steppe]

if you look at the original image the data repeats in the exact same format (the Statistics for row repeats a bunch of times with Feb. 2017 data, then repeats again for March, and repeats again for April, etc)

the original CSV only has three columns

[plush egret]

oohh

theres a dplyr for this i remember

i guess anything can do

[quartz flare]

Ah I see it now

[little steppe]

it's really effing annoying for data analysis

[plush egret]

can you share the data

[little steppe]

governments love using this format for data and it's so bad for researchers

[plush egret]

https://tidyr.tidyverse.org/reference/pivot_wider.html

here's the tool im thinking

[quartz flare]

Literally

[plush egret]

but im sure theres an equivalent

[little steppe]

yeah r is fine

i'll go have a futz with it

[plush egret]

lemme know itd be fun to review

i imagine collapsing the yearmonth into year first is easier

[full forum]

@little steppe Has your question been resolved?

[little steppe]

^^ still working

[full forum]

@little steppe Has your question been resolved?

[little steppe]

^^ still working

@plush egret

.close

[full forum]

Channel closed

Closed by @little steppe

Use .reopen if this was a mistake.

[plush egret]

congrats

R is pretty nice once you get used to piping

or whatever they call %>%

its been a few years

[little steppe]

why can governments not give data in nice easy-to-read formats

[plush egret]

your person in the government is probably a person who barely figured out how to make a spreadsheet

i have learned

they dont have any training in standards or normal forms or anything

they got told hey were doing open data now and figured it out as best they could

[little steppe]

yep

[full forum]

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[lime rover]

Help me solve this cubic equation:
x³+3x=5

[lapis holly]

Use Cardano formula.