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myme
@myme

f’ is dependent directly on the value of delta x, and it is not to be confused with delta y, delta f, dy, dx, df, x’, or y’ Confusing?
2024-02-25 16:12:15.498
Grayson Kellogg
@grayson

@myme Not explain the derivative itself, explain the definition of a derivative and why it represents the instantaneous rate of change on a given function f.
2024-02-24 21:26:50.557
myme
@myme

The derivative can be thought of as the comparison between two points of f on a graph.
2024-02-24 16:11:05.588
Grayson Kellogg
@grayson

Challenge 18:
Explain and prove the formal definition of a derivative in an intuitive way.
Formal definition of a derivative:
fx=limΔx0fx+ΔxfxΔx
2024-02-23 19:22:44.733
myme
@myme

First i would draw a 6 inch line
Second i would draw a line of arbitrary length on the middle of this line
Third i would draw a line 6 inches to this halfway line from one of the edges
Then i would join this line to the other end of the first line.
2024-02-11 23:59:37.235
myme
@myme

I found it on the ai websites
2024-02-11 23:56:59.727
myme
@myme

Problem:
Consider a geometric arrangement of vertices and edges in a mathematical graph. The beauty of this graph is to be quantified using a mathematical expression that encapsulates the elegance, symmetry, and creativity inherent in its structure. The problem encompasses the task of formulating a mathematical function that captures the essence of beauty within the graph, allowing for a comprehensive analysis of its aesthetic properties.
Solution:
To quantify the beauty of the mathematical graph, we embark on a journey that involves the exploration of various mathematical concepts and principles that underpin the inherent beauty of its structure. Our endeavor is to construct a mathematical function that encapsulates the profound elegance, harmony, and creativity embodied within the graph, allowing us to unravel the intrinsic beauty that permeates through its geometric arrangement of vertices and edges.
Firstly, let us delve into the realm of symmetry, a fundamental concept that often serves as a beacon of beauty within mathematical structures. Symmetry within the graph can be quantified through the examination of its symmetrical properties, including reflective symmetry, rotational symmetry, and translational symmetry. We can define a parameter S to represent the degree of symmetry within the graph, with a higher value of S indicating a greater level of symmetry, thereby contributing to its overall aesthetic appeal.
Next, we turn our attention to the elegance and simplicity inherent in the geometric arrangement of the graph. The pursuit of simplicity within the graph can be quantified through the assessment of its structural complexity, connectivity, and compactness. Let us introduce a parameter E to measure the elegance of the graph, with a higher value of E corresponding to a more elegant and structurally simple arrangement, thereby contributing to its aesthetic allure.
Furthermore, we explore the interplay of creativity and innovation within the graph, reflecting the intuitive leaps and ingenuity that underpin its geometric construction. The creative spirit inherent in the graph can be quantified through the assessment of novel geometric patterns, innovative structural motifs, and transformative design elements. We introduce a parameter C to represent the level of creativity within the graph, with a higher value of C signifying a greater degree of creative innovation, thereby enhancing its overall aesthetic appeal.
In addition to the abstract beauty that arises from the underlying structure of the graph, we consider the application of mathematical concepts to real-world phenomena, adding another layer of beauty to its geometric discourse. The ability of the graph to elegantly model and elucidate complex natural phenomena serves as a testament to the intrinsic beauty and power of its mathematical abstraction. Let us introduce a parameter A to represent the applicability of the graph to real-world phenomena, with a higher value of A indicating a greater degree of mathematical abstraction that enhances its aesthetic allure.
With these parameters in place, we construct a mathematical function B that quantifies the overall beauty of the graph, incorporating the parameters of symmetry (S), elegance (E), creativity (C), and applicability (A). The function B is defined as follows:
B(S, E, C, A) = k₁S + k₂E + k₃C + k₄A
Where k₁, k₂, k₃, and k₄ are weighting factors that reflect the relative importance of each parameter in contributing to the overall beauty of the graph. These weighting factors are determined based on the significance of symmetry, elegance, creativity, and applicability within the context of the specific graph under consideration.
Having formulated the mathematical function B that quantifies the beauty of the graph, we proceed to analyze its aesthetic properties by evaluating the values of the parameters S, E, C, and A within the context of the graph's geometric arrangement. By computing the values of these parameters and subsequently plugging them into the function B, we obtain a quantitative measure of the graph's beauty, offering a comprehensive analysis of its aesthetic allure based on the interplay of symmetry, elegance, creativity, and applicability.
In conclusion, the formulation of the mathematical function B provides a powerful framework for quantifying the beauty of the mathematical graph, allowing for a comprehensive analysis of its aesthetic properties based on the interplay of symmetry, elegance, creativity, and applicability. This mathematical approach to beauty offers a profound insight into the intrinsic allure of the graph, encapsulating the profound elegance, harmony, and creativity that underpin its geometric structure. Just as a masterful symphony captivates the soul with its harmonious interplay of melodies, the mathematical function B invites us to marvel at the captivating interplay of symmetry, elegance, creativity, and applicability that animates the beauty of the graph.
2024-02-11 23:56:31.855
Grayson Kellogg
@grayson

@myme That’s okay, can you describe how you would do it?
2024-02-05 23:52:33.771
myme
@myme

@grayson yes, but cant post pics on here
2024-02-03 14:44:40.203
Grayson Kellogg
@grayson

Challenge 17:
Can you construct an equilateral triangle using only a pencil, paper, and a ruler?
2024-02-02 03:34:30.894
myme
@myme

Weekly challenge: how do u describe the formation and kinematics of a 6 star solar system? Also who here is a gemini? https://en.wikipedia.org/wiki/Castor_(star)
2024-01-13 23:14:47.236
myme
@myme

Sorry, its because (2k+1)mod2=1,/0.
2023-12-30 16:04:51.948
myme
@myme

Its because 3n mod 2 equals 1 and not 0.
2023-12-30 16:03:37.065
Grayson Kellogg
@grayson

Task 16 (not original):
• There are three lights where two of them are on, and one are off, in the sequence ON, OFF, ON.
• On each turn you can flip the state of a pair of lights. They don’t have to be adjacent. For example, you could switch ON OFF ON to OFF OFF OFF by flipping the two lights that are on. When flipped, lights that are on turn off, and lights that are off turn on.
• You can do this three times. For example, a legal sequence would be ON OFF ON → OFF ON ON → OFF OFF OFF → ON ON OFF. The initial state ON OFF ON does not count as a move.
• To win the exercise, you would have to, by the end of your three turns, end with ON ON ON.
→ Prove this is not possible.
(Task inspired by a YouTube video.)
2023-12-29 07:15:46.876
myme
@myme

A historical origins of christmas documentary https://www.youtube.com/watch?v=Ots9y_xcaX8
2023-12-25 14:54:33.338
myme
@myme

https://gizmodo.com/uranus-image-webb-telescope-rings-moons-1851107986
2023-12-20 14:02:46.652
myme
@myme

Todays sunday sermon will be on entropy, please contribute to the sermon. https://www.youtube.com/watch?v=GOrWy_yNBvY
2023-12-03 20:20:50.698
myme
@myme

Welcome akwen and shani, Todays sunday sermon will be on how public disclosure is an important part of science in the way it operates, and how it works. https://www.sciencedirect.com/science/article/abs/pii/S0048733317300392
2023-11-26 13:40:46.183
myme
@myme

@grayson thats a good one! Link to example. Anyone else?
2023-11-21 14:55:21.918
Grayson Kellogg
@grayson

@myme sound waves
2023-11-21 02:56:11.097
myme
@myme

Todays sunday topic will be on the geometry if sine. Can u list some applications of this function? https://mathworld.wolfram.com/Sine.html
2023-11-19 14:57:07.206
myme
@myme

This ai rewrote its own program, how was it able to do that? https://www.youtube.com/watch?v=wPaSW8yZxZA
2023-11-13 21:44:54.236
myme
@myme

https://www.theguardian.com/science/2023/nov/05/how-maths-can-help-you-win-at-everything?utm_source=pocket-newtab-en-us
2023-11-09 14:39:24.539
myme
@myme

Hello, its sunday again, todays sunday science topic will be on accurate formation of quantum depictions. https://www.youtube.com/watch?v=brQQV-qPGrQ https://www.youtube.com/watch?v=wMw_Nj_AWGc
2023-11-05 18:57:25.868
Grayson Kellogg
@grayson

@p88889
2xdx=x2+C
2023-11-04 02:28:34.980
Tânia Mara Tortola
@p88889

What does 2xdx equal?
2023-11-03 23:50:29.270
Grayson Kellogg
@grayson

@myme The description says that they made a bot analyze tons of horror movies and then create its own.
2023-11-03 15:18:06.333
myme
@myme

This short generated by netflix is 100% mathematically generated. https://www.youtube.com/watch?v=WZzbxNoMjGM can anyone here tell us how it is able to do this?
2023-11-03 03:54:38.782
myme
@myme

https://www.msn.com/en-us/news/technology/a-robot-ceo-is-running-an-entire-company/ar-AA1hibi5
2023-10-30 21:28:10.358
myme
@myme

Nobody answered last weeks sunday sermon, todays sunday sermon will be on newton raphsen iteration. Please provide a worked out application for this in thermodybamics. https://math.libretexts.org/Under_Construction/Numerical_Methods_with_Applications_(Kaw)/3%3A_Nonlinear_Equations/3.04%3A_Newton-Raphson_Method_for_Solving_a_Nonlinear_Equation
2023-10-29 19:51:43.523
myme
@myme

Todays sunday science sermon will be on science as a religion. https://www.psychologytoday.com/us/basics/terror-management-theory comment like share. Can there be such a thing as radical science?
2023-10-22 18:13:51.924
Grayson Kellogg
@grayson

@luis 5
2023-10-22 14:57:05.890
Grayson Kellogg
@grayson

@luis 81
2023-10-22 14:56:49.659
Alvarez Rodriguez
@luis

3632
2023-10-22 08:42:51.827
Alvarez Rodriguez
@luis

522
2023-10-22 04:58:26.294
myme
@myme

Because fallacy starts with f for false, and theory starts with t for true.
2023-10-18 15:12:33.224
myme
@myme

@grayson thats what im saying. U need parameters. Or else u will have a fallacy and not a theory.
2023-10-18 15:11:03.329
Grayson Kellogg
@grayson

@myme Wait… how can a board be infinite in size if it is also made of wood? There is not an infinite amount of wood nor an infinite amount of space, so the board can’t be infinite if it is also physically wood.
2023-10-18 06:21:25.243
Grayson Kellogg
@grayson

@myme I don’t know then. What is the solution?
2023-10-18 06:20:28.347
myme
@myme

@grayson this board is certainly not infinite in size. Chess boards usually rnt infinite in size.
2023-10-17 19:34:07.666
Grayson Kellogg
@grayson

Question 15:
Find the derivative of x3 using the definition of the derivative, and show your work.
(Do not use the derivative rules. Instead, use the definition of the derivative.)
Definition of the derivative:
fx=limh0fx+hfxh
2023-10-16 23:52:29.732
Grayson Kellogg
@grayson

@myme chess.com
2023-10-15 23:36:34.876
myme
@myme

Give me an example of a board game that is made out of wood that is sold in stores that is infinite in size. Please provide link to that.
2023-10-15 15:05:57.713
Grayson Kellogg
@grayson

@myme Ok, I finally found a website that converts the PDF. I deleted the other link, try this one instead for the examples: https://shorturl.at/cezPY
2023-10-12 01:08:15.991
Grayson Kellogg
@grayson

@myme I created a simple paper outlining the rules. I don’t know how to create the PDF as a URL like you did, so I will put the document link directly: https://docs.google.com/document/d/1FVzuPDVbiaDoKsOWUWHYOrF9KhX1G_-8ovaYKT6kNHE/edit?usp=sharing
2023-10-11 23:43:44.599
Grayson Kellogg
@grayson

@myme No. The board is infinite in size.
2023-10-11 22:50:11.693
myme
@myme

@grayson wouldnt it depend on the size of the board?
2023-10-11 16:58:58.997
Grayson Kellogg
@grayson

@myme Any node that was derived from a previous one has an arrow if its parent is still present. The arrow connects its parent to it. However, if one of the nodes the arrow is connecting is destroyed by the second player, the arrow itself is also destroyed.
For example:
If a node A created a node B, then the map might look like:
A → B
However, if B created A, then:
B → A
However, if the second player destroys one of those nodes that the arrow is connecting, the arrow itself is removed.
So if they destroy node A:
B
Or if they destroy B:
A
2023-10-10 05:02:20.398
myme
@myme

@grayson what causes an arrow to point in a direction?
2023-10-10 02:40:25.675
Grayson Kellogg
@grayson

Question 14:
Start your Monday with this fun but complex puzzle!
Imagine a graph with two node colors: red and blue. Let K and d be natural numbers.¹
(¹For the purposes of this exercise, zero should not be considered a natural number.)
Start with a single red node.
Each step, any red nodes with no arrows going from them create d new blue nodes. At the same time, any blue nodes (excluding the ones just created) with no arrows pointing from them create one new red node. Every node created by another node has an arrow going from its parent to it. This is player A’s turn.
On player B’s turn, they can “take” (remove) up to K nodes. Removing a node also removes any arrows pointing to or from it, and nodes can be reactivated this way.
Player B wins if they drive the population to extinction (if they remove all of the nodes.)
Player A wins if Player B cannot win (if the population will avoid extinction forever.) A converging population (e.g. one that cannot diverge to infinity but will never go extinct) still counts as a win for Player A.
1. Try the classic variation of this problem with d = 8. Assuming optimal play by Player B, what is the maximum value we can set for K, where K ∈ ℕ, where Player A will always win, no matter what moves Player B makes?
2. More importantly, can we create a function K(d) in terms of d that will find the maximum winnable value of K for us for any d ∈ ℕ?
2023-10-09 01:48:40.113
myme
@myme

Hi new people, tj, albertus, aisha, welcome to final equation. Also join wolfram and momath, comment on here for once, do my assignments, post your own assignments, tell us your backgrounds.
2023-10-08 15:51:31.658
myme
@myme

Hello people, its sunday again, happy sunday, todays sunday sermon will be on this puzzle. How many solutions are there to this puzzle? Can u list them and prove why each of them is a solution? https://browse.arxiv.org/pdf/0911.2567.pdf
2023-10-08 15:49:46.905
myme
@myme

https://www.scientificamerican.com/article/why-do-we-forget-so-many-of-our-dreams/?utm_source=pocket-newtab-en-us
2023-10-02 22:05:13.846
myme
@myme

Hi bob i meant, typo.
2023-10-02 22:04:25.452
myme
@myme

Hi bon
2023-10-02 14:06:13.126
myme
@myme

Hello, happy sunday, today is sunday again, todays sunday challenge is to count the number of the different ways math is used in this video. https://www.youtube.com/watch?v=8n_zpCUWGvI
2023-10-01 16:56:22.120
Grayson Kellogg
@grayson

Question 13:
What is the formal definition of the derivative?
2023-09-30 19:47:21.003
Grayson Kellogg
@grayson

@myme If it is too easy, then what is the solution?
2023-09-29 19:35:37.409
myme
@myme

@grayson this one is too easy. I dont believe in imaginary numbers anyway. Numbers are imaginary in general and only exist in theory.
2023-09-29 13:17:01.133
Grayson Kellogg
@grayson

Question 12:
Find a function that takes in a complex number as input and outputs a unique real number.
(Every complex number should output a unique real number, no x or y values should be repeated.)
2023-09-26 03:37:25.060
myme
@myme

It will be up to u to create a sunday sermon today.
2023-09-24 14:45:44.863
Grayson Kellogg
@grayson

Question 11
How does the “Proofs” section of this app work?
2023-09-20 04:45:10.540
myme
@myme

Greetings, everybody here, because i know youre here, todays sunday sermon will be on tile theory. https://en.wikipedia.org/wiki/Convex_uniform_honeycomb, comment, like, share, what do u think, tell your friends, post something for once. The only other person still active on here is still in middle school.
2023-09-17 15:36:01.916
myme
@myme

@grayson another hint https://www.youtube.com/watch?v=8DBhTXM_Br4
2023-09-14 16:47:23.728
Grayson Kellogg
@grayson

Question 10:
What are three things the bifurcation diagram represents?
For a hint, use this YouTube link: https://youtu.be/ovJcsL7vyrk?si=EhHes7nWbNl7zzxQ
2023-09-14 14:17:41.323
myme
@myme

@grayson well the answer isnt 8pi cm.
2023-09-13 03:21:34.338
Grayson Kellogg
@grayson

@myme I thought you were a polymath / multi modular mathematician.
2023-09-12 03:38:25.062
myme
@myme

@grayson please explain the answer in detail. dont limit your options. Im still a hobby math.
2023-09-11 21:50:38.023
Grayson Kellogg
@grayson

@myme I’m thinking about getting a job as a mathematician. Is it worth it?
2023-09-11 06:41:04.651
Grayson Kellogg
@grayson

@myme Sorry, but that is incorrect.
2023-09-11 06:37:24.217
myme
@myme

@grayson 2^((x+1)/2)^((x+1)/2)
2023-09-11 02:46:00.380
Grayson Kellogg
@grayson

@myme
fx=2x2+11+sgnx2
2023-09-11 00:08:39.278
myme
@myme

@grayson o wait a minute, u were asking how its related to psychics, routinely exhibit the ability to behave as a group even if some of the members of a single hive are separated by hundreds of miles. Whales also communicate over hundreds of miles through sonar through water, plants can communicate over hundreds of miles through hormones, but bees dont use either to do this, and it seems instantaneous.
2023-09-10 17:39:01.507
myme
@myme

@grayson supersymmetry is actually a symptom of fractal geometry, which has a major presence in physics. Supersymmetry is not inimical to physics itself, it is a purely natural phenomenon. Which leads me to the topic of quantum geometry, rather than quantum physics.
2023-09-10 17:35:51.258
myme
@myme

@grayson
the volume of a sphere is (4/3)pi*(r^3), the volume of a cube is (r^3).
(4/3)pi*(r2^3)=2(r1^3), simplify
(r2^3)=((3*pi)/2)(r1^3), r1=1, r1^3=1,
r2 =(3pi/2)^(1/3).
2023-09-10 17:30:53.912
Grayson Kellogg
@grayson

@myme Can you tell me how bees are related to psychics? I’m watching the video and it doesn’t make sense.
2023-09-10 17:25:58.512
Grayson Kellogg
@grayson

@myme Then, what is the right answer? And show your work.
2023-09-10 17:06:07.059
myme
@myme

Hello chat, today is sunday, happy sunday again, todays sunday sermon will be on supersymmetry as a psychic phenomenon. https://www.youtube.com/watch?v=NcZn1JspgrY
2023-09-10 16:46:07.770
myme
@myme

@grayson no, thats wrong.
2023-09-10 16:46:01.105
Grayson Kellogg
@grayson

@myme Volume of a sphere: V = 4πr³
Volume of cube = 1cm³
Since the sphere is double the volume of the cube (2cm³) we see
2cm³ = 4πr
Solve for r
2/r cm³ = 4π
Multiply both sides by 2
r = 2(4π)
r = 8π cm
2023-09-09 18:11:44.031
myme
@myme

A sphere has exactly double the volume of a given cube, which is 1cm3, What is the radius of this sphere?
2023-09-09 04:24:26.463
myme
@myme

@grayson because each person needs all 5 parts. It is a stalemate once each person gets at least 1 part. And nobody else is on here? Seriously?
2023-09-05 14:27:04.096
Grayson Kellogg
@grayson

Problem 9:
Logical Thinking, Easy
Imagine two people after an object split into five parts. To win, a person needs all five parts. One person gets two and the other gets one. This situation is a stalemate. Why?
2023-09-04 19:54:56.620
myme
@myme

Hello, happy sunday, its sunday again, todays lecture will be on the philosophy of science, watch, share, apply it to your lives, like. Explore similar videos. https://www.youtube.com/watch?v=tP8teUgZcBY
2023-09-03 14:55:31.729
Grayson Kellogg
@grayson

I have a problem 9 to post but I am leaving Sundays free for @myme’s sermons. I will wait until Monday.
2023-09-03 06:41:44.603
myme
@myme

@grayson it contains the criteria.
2023-09-03 02:25:10.806
Grayson Kellogg
@grayson

@myme But it meets the criteria.
2023-09-02 21:17:58.918
myme
@myme

@grayson too general
2023-09-02 10:26:58.625
Grayson Kellogg
@grayson

@myme Mathematics.
2023-09-02 01:18:57.714
myme
@myme

Give me an example of a system that is both quantum and logical.
2023-09-01 14:59:09.668
myme
@myme

@grayson give me an example of a system that is both quantum and logical.
2023-09-01 14:58:34.522
myme
@myme

@grayson it would be reachable to someone who can paddle for many thousands of years
2023-08-28 14:30:12.593
Grayson Kellogg
@grayson

@myme
I’m confused about the Fermi Paradox.
If the universe is infinite: there will eventually be more life somewhere in the universe, whether inside the observable universe or out in the unobservable.
However, this does not imply the life will be anywhere near us. They could be somewhere so far away that they are essentially unreachable.
Therefore, the Fermi Paradox is not a paradox and implies the existence of alien life.□
2023-08-28 04:09:21.205
Grayson Kellogg
@grayson

@myme I see the misunderstanding, I said the derivative where x is not an even natural number was zero. This is to ensure the function is not continuous, jumping up to its double instead of smoothly increasing.
2023-08-27 16:59:02.280
Grayson Kellogg
@grayson

@myme I said f(0)=2. This means inputting zero into the function gives 2 as output.
2023-08-27 16:54:55.152
myme
@myme

Hello, faithful people, its sunday, happy sunday again. Todays sunday sermon will be a discussion of paradoxes in logic. This discussion is not relegated to this 1 chat, engage your friends, post on your channels, have open discussion. https://www.youtube.com/watch?v=AqkMykYQ7eU
2023-08-27 14:31:40.565
myme
@myme

@grayson but u said that its zero when x is not an integer. The only other option here would have to be an infinitely long list of x and y values.
2023-08-27 14:29:59.090
Grayson Kellogg
@grayson

@myme Great answer, but there are a few problems:
That looks like computer programming, plus it can’t be a conditional function. The problem states has to be one non-piecewise function that can work for all real values.
Thank you for attempting the problem, and I’m sorry if the instructions weren’t clear enough.
2023-08-27 06:29:37.256
myme
@myme

@grayson (int y) = 2^(int(x+1)), else: (float y)=0.
2023-08-27 05:24:20.523
Grayson Kellogg
@grayson

Hello, happy Saturday!
As a warm-up for @myme’s sermon on Sunday, try this classic but deceptively easy exercise:
Problem 8:
Find me a non-piecewise function fx that meets all of the following conditions:
f0=2.
For every even natural number (2, 4, 6…) the range doubles. (2, 4, 8, 16…)
For all a<0:fa=1
The function should not be continuous. It should jump at every even natural number up to its double.
At every point where the function does NOT jump, the derivative at that point should equal zero.
2023-08-26 18:37:50.784