Z* is a bad notation for Z\{0}. Usually, the * means the set of invertible elements. In Q and R, all numbers except zero are, but in Z, only ±1 are invertible.

ffs turn off the voice changer please

funny enough, if you are using the wheel of real fractions, 1/x actually *is* continuous at x=0, which is possible because this algebra satisfies -∞ = +∞.

Ecclesiastes 7:3 Sorrow is better than laughter; it may sadden your face, but it sharpens your understanding. Proverbs 14:13 Laughter might hide your sadness. But when the laughter is gone, the sadness remains. If you want to know the Truth follow Jesus.

I don't have any grapes, okay?

For what

Your a mathematician you shouldln't be involved in such problems or not most of the time at least focus about the main structure of math which is analysis and set theory and geometry best of luck those are to some extent are only mere puzzles.

“Got any grapes?” ahh voice

It is called rotation matrix

My god this voice

Cool, now integrate them

How are you now?

As an Algebra 2 student I am flabbergasted by the ludicrous graphs that were previewed.

Easy: parameterization

The method I have always learned is convert the graph to vectors and apply a linear transformation, which basically does the same thing.

If you have leart rotate metrix, you can easily get the formula what video get. And you can let u= xcost-ysint v= xsint+ycost This is more readable.

I skip most of the yap to go to the rotating functions

Video compression go burr

This was freaking beautiful.

The rotation would change y=f(x) into g(x,y)=0

What if I have a complex space for the inputs and outputs, should still work yeah? I want to rotate the Riemann Zeta function by 90 degrees

You explained to Principe of Ray Tracing by the way!

You talk about parametric graphs, OK. But what about rotating a function for real, in the form y= f(x), since it ist definite?

How do you make this work in Desmos? Is there a specific way it needs to be written?

u sound like a fking stereotype lol 😂

Well my graphics calculator certainly does Not let me put values of y on both sides of the function and then draw a graph; It's seams pretty set at Y=... As it's only form. So though the principle in this video seams interesting it's clear you have software which lets you do that, which the standard maths stuff doesn't. Both the software and calculator I have also specifically will not process multiple y values equalling a single x value. Hence the difference in plotting √X to X^2 ; √X should just be the 90° pivot of x^2, but it won't produce the two values of y no matter how I present it (i.e. X^0.5 Vs √X)

I can't forget that this guy created a blackhole with graphs..😵

MOB

I found an easy way to put it into Desmos, have different equations: defining the original function before rotation (“f(x)=…”), defining a variable (“b=…”) and the function after rotation. And preferably, put it on “degree” mode. For the parabola at a 45º angle, it would be: f(x)=x^2 b=45 x*sin(b)+y*cos(b) = f(x*cos(b) - y*sin(b)) Change variable “b” to however many degrees rotated you want and change the “f(x)=…” equation to whatever you need to change it to and the rotated equation will update with it. Setting it up like this will also make it so u only have to update less things whenever you want to make a change

Bro talks like "🤓"

Infinite is a set of numbers but infinite numbers are not algebraic. Ex: ...123123.123123... is an infinite number.

Quite informative & humorous

Thank you so much I needed this for math I’m cooked bro

what is the mob function???? i cannot find anything about it.

Beautiful

You multiply it Oh. Well, to rotate it you have to figure out that yourself.

I figured this out myself and i m low key proud on that(i m asian)

Ин раша ви лёрн абаут параболас ин севенф грейд

we makin it out precalc with this one ‼️‼️‼️🗣️🗣️🔥🗣️🔥🗣️🔥🗣️🔥🔥🗣️🔥

Sitting in my freshman math class, I came up with this projection concept but I had no idea this existed. My approach was evaluating how complex numbers would work with this creating a spherical or torrid geometry. The curvature would be flat because the number line extends to infinity. In other words, this concept as a "number line" would be the same for finite ranges.

Fighting equations 😂😂

"MOB, I don't even know what MOB means"

16:24 desmos 3d: hey thats part of my job

(t cos R+f(t) sin R,t sin R-f(t) cos R) Rotates stuff Make R= anything Make a normal funct like x^2 make = f(x) giving f(x)=x^2 and boom rotation

11:29 my computer would turn itself inside out trying to run that in google chrome

This reminded me, that in computer graphics, coordinates are represented using matrices and you can compute rotations very easily. If rotation is in angles however, this method is required.

how can I rotate "y=sin(x^{2})"?

I wrote a complex number lib, and you can just multiply the function in parametric form by (cos θ, sin θ). Works like a charm.

200th comment :)

but what about some specific angles like 266deg or 537 deg or 2rad