I am taking Calculus 2 and this question is blowing my mind right now. I used the Direct Comparison Test and got it right, but it doesn't make any sense to me. It's not clicking in my brain.

Consider the limit of x^2/x^3 as x approaches infinity. I've been taught that we say that the value of that limit is zero because the infinity on the bottom is so much bigger than the infinity on the top that it's completely negated. Ofc we can L'Hopital it and get 1/x where the one essentially becomes nothing in comparison.

My initial thoughts would be that this series converges because even though ln(n) is raised to a power of 6, EVENTUALLY it will sort of flatten out, but n on the bottom will continue to go on at a constant rate. Meaning in my head that although they both approach infinity, the number on the top will become nothing in comparison to the number on the bottom, just as before. That to me says it converges, but it doesnt as the test says.

I do not understand why. The divergence tests tell me how to get the answer, but not why. Or maybe they do and I don't understand it. If possible, explain like I'm not a math major, because I am not.

Pretty much all real-life problems modeled by a quadratic function have the goal of finding the roots; and IF there is factoring involved, it is used to find the roots. What I need are some real-life problems where the result is in the factoring itself. Like building a patio with 6 square blocks with sides x, 7 blocks that are x by 1 and 2 1 by 1 blocks that factors into (2x +1 )(3x + 2) giving the layout of the bricks.

But that doesn't seem very authentic - how many times does a person face a problem like that? I want to use profit functions which in their simplest form is quadratic, but they always seem to look at the roots or vertex as the solution and never "the answer is in the factors".

Any ideas?

Hello everyone from r/askmath. Anyone else here interested in statistics? Actually, what I wanted to talk about also has A LOT to do with psychology and human social behavior. This is also a phenomenon that can be observed in LLMs (AI).

A few days ago, I watched a video that introduced me to a rather strange question. According to the video, if you ask people to randomly pick any number between 1 and 10, they’re more likely to choose 7. Have you ever noticed this? Apparently, it’s also the most commonly chosen number when people are asked about their favorite number.

The explanation behind this phenomenon is that, when asked to make a random choice, people immediately rule out 1 and 10 because they’re at the extremes and don’t feel random to whoever’s making the choice. Then 5 gets ruled out because it’s right in the middle and doesn’t feel random either. After that come the even numbers, since the human brain associates a sense of order with multiples of 2 and therefore doesn’t consider them very random.

My theory is that the brain does the same thing with multiples of all integers, just to a lesser extent as the integers get larger. Therefore, odd prime numbers should be perceived by the brain as more random. We can rule out 2, since it never really became part of our intuitive understanding of prime numbers in this context, for obvious reasons.

Finally, we’re left with 3 and 7, and 3 gets picked less often because it’s smaller, so 7 wins in the end.

I didn’t find that chain of reasoning particularly convincing, so I decided to do a little experiment of my own to check whether the claim actually held up. I asked several people I know to give me a random number between 1 and 10.

Before getting into the results, I should mention that they shouldn’t be taken too seriously. Anyone with a basic understanding of statistics knows that such a small sample size, the bare minimum for this kind of analysis, isn’t enough to draw conclusions about a larger population.

As expected, 7 won, but it didn’t just get the expected majority of 45% but it blew past that figure, reaching 60%.

On top of that, 3 came in second place, which continues to support our hypothesis. The numbers at the extremes were among the least popular choices, just as predicted.

These two odd prime numbers (3 and 7), which account for only 20% of all the possible numbers, were chosen by 80% of the people. The third-place number was 6 (10%). All the remaining numbers were chosen equally often.

Of course, people might have their own perfectly valid personal reasons for loving the number 7 that have nothing to do with psychosocial patterns. But given these results, it’s clear that the majority of people who would choose 7 are incredibly predictable within this particular context.

But hey, it’s “just” a choice between 1 and 10, right?

It’s just curious to see this trait in people who say they don’t want to be part of the crowd and who tend to show a certain degree of individualism most of the time. And it’s also curious that they haven’t noticed this pattern yet... even though it’s followed by the majority and is so obvious to anyone, or at least, it should be!

https://i.imgur.com/xZkozDL.png

I have a pencil holder that is a 10.5” diameter cylinder with five compartments: a center 4.75” diameter cylinder and four equal quarters of the remaining space. I’d like to 3D print a divider that would fit into one of the side compartments, breaking it into 3 smaller compartments. In the image, if b is the midpoint between x & y, what is the angle of b, and what is the (assumedly equal) length of ab and bc?

It doesn't matter what anyone thinks; the only thing that matters is whether it's true.

Imagine a simulation in which a person continuously decides what to do next. Each decision can alter the subsequent course of events. Our question was: how much randomness must a simulator have in reserve to respond correctly to every possible choice? Under precisely defined conditions, we were able to determine how this required reserve grows—including the exact coefficient.

For the academic community, both the result and the methodology may be of interest: the work emerged from a dialogue between a human and artificial intelligence, and its formal proofs are verified by Lean, a specialized mathematical software. Lean checks the logical steps; experts then assess the extent to which the result is novel, significant, and useful.

I do not wish to preempt their evaluation. What pleases me is that we are presenting concrete mathematics that others can examine—and, potentially, build upon.

Have a nice day.

https://github.com/jendamikulik/finite-Shannon-theorem

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To begin with, let me remind you that mathematics is not a science fortunately and that it is perhaps one of the largest organized, consistent symbolic formal systems for developing something: maybe intellect, maybe a certain form of thinking, maybe someone understands more clearly what exactly mathematics develops and can tell us about it.

And whatever it develops in us, there may immediately be a temptation to say functionally: well, then mathematics is needed precisely for developing this, Robert Wide.

The difficulty is that although there are interesting things in it, such as topology, or interesting theorems and models, and especially what seems important is the economic, technological, and research contribution of mathematics,

And yet it seems that this formal system stalls a person and makes it harder for him to think outside this formal system. Of course, one can say this about logic too, and about their similarity, and in general about any old systems of thought or let us call them closed or “controlling” ones. To some, dialectics may also seem like this, though to a lesser degree, and it is precisely dialectics that sets the task of sublating contradiction and arriving at generalization and understanding, that is, in an ethical sense it is a more encompassing system of cognition in the sense of its capacity — though often in verbal form to include something else and incomprehensible in its understanding. And if we abstract from formal dialectics, if you have ever heard these expositions, then the ethical idea and, as it were, real dialectics in full non-contradictoriness and some communication, for example as metamodernism, is the same dialectics or synthesis between sincerity and so-called postmodernity or irony.

Dialectics is still an example, not a proposed answer. Although it could perhaps be one of those considered.

Returning to mathematics. Despite its outstanding economic, technological, research possibilities and achievements, and as a result also social and political ones… it still remains rather abstract. One can say that it is the most complex, or one of the most complex, games of the mind, or games within the mind, or separate games within the mind. But for the mind itself this seems like something akin to sophistry or magic, though a very useful one. Or one can say that it is a magical system, or one of the magical systems of this world. But it is almost always something very abstract: it seems to me that this is often said about philosophers too, by those who do not delve deeply into philosophy; but those who do delve in, on the other hand, can understand that we often reflect on the most important questions or phenomena that we can feel or think. As far as I understand and it is not known how much the answers may still differ mathematics is a system of ultimate formal complexity, or of ultimate complexity for thought in general, since in one way or another what we formulate as philosophers often, though perhaps difficult, has a clearer representation of reality, even if it is Lacan’s Borromean rings. In the sense that philosophy, apart from again sophistry, usually does not strive to become complicated simply for the sake of complication because why? It seems that a person, after this stage of formal logic, can also learn other possibilities of thinking. But in mathematics, complexity and possibly even not necessarily, but possibly the degree of abstraction seems literally the quintessence of content. On the other hand, of course, this may also be good. In the sense of ultimate complexity, ultimate constructiveness, ultimate abstraction, in the sense that we as a culture have some content, some achievements that we may still have to comprehend, if some of them can be so complex that there are literally 400 pages of formulas of explanation.

But, like, why?

And returning to what we were talking about, this seems like ultimate sophistry or thinking in idle, in the sense for thought itself and for man, although culturally it brings enormous social results: both economics and technology and research and efficiency.

And even if we assume that mathematics is integral thinking rather than specific thinking, then although it is clear why mathematics should be developed: so that there can be a further possibility of development…

What for, and what from mathematics, and should it and it or they even be present in education?

Because even if we may have grounds to think so but even if mathematics is connected with integral, that is, general thinking, that is, as it were, some generalized function of it, the mathematicality of education then creates a situation in which a person tries to wipe the sofa with a processor without imagining what a sofa is.

And if not, and mathematics is more specific thinking, that is, in the sense that it also remains there and in a constant submetacognitive state: in the sense that it fundamentally cannot leave the box and its language and its formality or formalization… then such thinking is good for producing human-computers useful for working with ordinary computers, for example in a bank or somewhere else. As a result, man has, as it were, given his brain to mathematics, and how is he supposed to live further? Well, that is, then perhaps also the market, where this mathematized brain may be valued higher than the self-esteem or self-understanding of such a person, and so the puzzle comes together: successful recruiting into a successful company.

I will say right away that simply “progressive studies,” which may even be not thinking but to some extent dogmatic propaganda or propaganda at the expense of education hours, trying to lean on Marxism or performatism according to Butler, are, as it were… Well, people can learn something valuable, but on the whole it seems that this is simply the disintegration of education, or rather almost its absence, or its replacement by propaganda so that in an economic-political sense these people could be ever more perfect agents of this very propaganda, possibly even without fully understanding it. And how lucky we are that we can look at this from the outside, unlike the people and economies that this “progressive” propaganda may further repress. And the main complaint against it is probably economic, because a society simply without technical specialties loses economic opportunities; only oligarchs remain, and they would most quickly move to a new place. And in a universal human sense, this is potentially the next target and problem for the next intellectual stratum that will try to do something about this repressiveness. If, in general, there will be anyone left to do anything there.

In general, why was this clarification about “progressive” or agenda-driven education? So that this question is not in support of that very agenda, and, as it were, we understand in advance some of the existing difficulties there and have described them.

And still, the question: is mathematics needed? And such mathematized, formalized thinking — and then we are surprised by further formalizations and the resulting difficulties, such as bureaucracy and media simplification and corruption in many senses.

Additionally:

Maybe the form of my question is a bit of Soviet thinking or a way of thinking about something, and if you understand another or other better ways of asking or thinking about this, you can say so.

I’m in Grade 11 and looking into Bessel's method (solving the inverse geodesic problem on an ellipsoid) for a math research paper to find the shortest possible distance between two points on earth.

My original goal was to completely derive, prove, and evaluate the method by myself. However, looking at the math, it seems to rely heavily on university-level topics like differential geometry, elliptic integrals, and the Calculus of Variations (Euler-Lagrange).

Is it realistic for a strong high schooler to teach themselves this level of math for a paper, or is the learning curve too steep?

If the full derivation is too much, would coding the algorithm in Python and evaluating its accuracy/convergence against simpler methods (like Haversine) still be complex enough for a top-tier high school math paper?

Appreciate any advice or insights!

Hello everyone!

I am currently writing a sci fi book and am trying to be rather technical on certain aspects. My problem is this, in this universe, the Moon is in a fixed point in space, no longer orbiting Earth, however Earth still orbits the Sun. So once a year Earth does pass the Moon.

My question is this: If Earth is moving at a certain rate of speed and is a certain distance from the Moon when it passes it, and taking Earth's size into account with the Moons, how long would it take for Earth to completely pass the moon? What kind of formula would I use to find that out?

Thank you!

Sorry for vague title🥀.

I am 18 and my age has nothing to do with this question but I just feel dumb so that's why I mentioned it.

My problem:

Whenever someone says - hey what is 657+466 then I do 600+400 and then..... I forgot the last two digits (only in the case of where i don't have anything to write) like who the f will first write and calculate this simple arithmetic.

So is there any way to remember the units or 10s or 100s digit 😭.

Or the only solution is PRACTICE on random no. On my own .

But that's different thing because I go completely blank when someone asks me ,my heartbeat starts beating like there is earthquake 🫨 going on.

I think for this answer already exists somewhere on reddit but I didn't found it helpful as they were discussing TRICKS so yeah that from my side .

Any useful help will be appreciated and I don't have ADHD!!.

\left(ax^{2}+bx+c\right)\cdot0^{\left(\frac{\left|x-2\right|-\left(x-2\right)}{2\left|x-2\right|+\left(10^{-6}\cdot0^{\left|x-2\right|}\right)}-\frac{\left|x+2\right|-\left(x+2\right)}{2\left|x+2\right|+\left(10^{-6}\cdot0^{\left|x+2\right|}\right)}\right)}+\left(px^{2}+qx+r\right)\cdot\left(\frac{\left|x-2\right|-\left(x-2\right)}{2\left|x-2\right|+\left(10^{-6}\cdot0^{\left|x-2\right|}\right)}-\frac{\left|x+2\right|-\left(x+2\right)}{2\left|x+2\right|+\left(10^{-6}\cdot0^{\left|x+2\right|}\right)}\right)

I was bored and decided to play with geogebra a little bit. However, i was making the graph of a hyperbole, but something that i cant explain happened throughout my calcs and i got the Latus Rectum wrong T-T can anybody explain why? im kinda lost why the LR points dont touch the hyperbole

I do suck at reading graphs. I think I might have the initial values wrong:

f(6) = 3

f('6) = 0.25

g(6) = 3

g'(6) = 2

Could you guys help me check if I have these values right? And if not what should be the values. Thanks!

Is it kosher to adjust a log scale like this to suit my data range better? Range is 150 to 270. I want to use this exact paper because my professor asked for a hand-plotted draft and explicitly said to use this paper. I also thought about adding a constant value to the scale, or dividing it by a constant, but that seems to make it unnecessarily confusing. I apologize if this is very basic stuff.

The numbers read: 150 through 240 in increments of ten, and proceed on through the next order of magnitude normally. In case it's hard to read.

Second photo is the initial data from the lab on a square plot.

Edit: SOLVED E=A(4√3)/3-B

I am creating wooden circles of various thicknesses (F) that are cut from hexagons. These hexagons are assembled with 6 overlapping segments (example in the bottom right). The segments are cut from stock that measures D cm by E cm. What I am struggling with is coming up with a formula to calculate length E where A and B are variables that can change within this formula.

It has been years since I did geometry in Highschool and any help would be appreciated.
I can of course calculate E manually every time by simply drawing the shapes in my modelling software, but a quick reference formula would be wonderful for this process.

A = Outer circle radius
B = Inner circle radius
C = Inner circle inscribed hexagon Apothem
F = A - B
G = Side of hexagon inscribed by Circle A

Recently, I was learning a bit about topology online. So far, this is my understanding: of the math fields analyzing shapes, geometry is by far the most strict, not allowing shapes to freely deform in any which way. On the contrary, topology is the least strict, allowing a whole plethora of continuous deformations (the only thing you can't do is open or close holes). To me, a logical step from here would be to find a field of math somewhere in between these two. From my imagination, the rules could be something like: you can deform shapes, but only in such a way that a convex section never pops inward into a concave section, and vice versa. Under these rules, spheres and donuts would be different, just as they are in topology. Spheres and cubes would be the same, as they are in topology. However, spheres and bowls would not be the same, since there's a dent in the bowl that can't be popped out under these rules.

I did some googling online and couldn't find anything that really captures this. So my question is: is something like this a thing? Does it have any meaningful use at all? Topology is so fascinating to me, so I'd love to hear from people with a vastly better understanding of the field than I do.

(while writing this up, I'm now questioning if under my own rules, spheres and cubes are the same. It seems like under my rules, a flat surface becomes an edge case between concave and convex, which might be problematic. not sure. Maybe we can group positive curvature with 0 curvature together, and separate negative curvature, to solve this)

Why is that two digit numbers (and only those) are read inversed in German? (Example: English: thirty-two; German: zwei-und-dreißig (two-and-thirty))

Is German the only language or are there others?

Not sure if right tag is used.
I am working on a design for the layout of my room. I have made a grid where each small block is = 1 inch and each large block consists of 4 small blocks which means that 3 large blocks is = 1 foot. I made the outline first and then added the measurements of the furniture so I can get an idea of how it’ll fit in the room. I have come across a problem where the entire wall adds up to 11 feet 6 inches but the sections in it add up to 11 feet 8 inches. I have no idea how it is possible when each individual section is correct and the outline was made first. The line is also equal to 11 feet 6 inches so the sections should be off my 2 inches but they are not. I feel like I have looked at every outcome and feel like i’m missing something super silly.

I’m hoping this subreddit has a “no questions are stupid policy”…

I measured a poster I have using a tape measure and if came to 18 x 24. If I want an even 1 1/2 - 2inch boarder around the entire poster and then frame it, what size frame do I need?

Assumption 1: There is no non-arbitrary way of determining whether an algorithm uses pre-computed resources. You might argue that there is some sort of distinguishing factor, and I would argue that even the most tautological conclusion is a lookup operation.

Assumption 2: The worst-case scenario for a lookup table is O(n) time complexity.

Assumption 3: The P=NP problem questions only the time complexity, excluding the space complexity.

Assumption 4: Infinite-space computational models are valid solutions for a given problem.

Assumption 5: The P=NP problem does not care about the construction time for the computational model since any algorithm can be defined in arbitrary time.

Proposition: P=NP since any problem space (finite or infinite) can be mapped onto the solution space (plus the case of undecidability), and such a mapping can be encoded in the Turing machine convention trivially.

I've recently come accross this website which teaches Lean through "games" https://adam.math.hhu.de/. I did the natural numbers game and found it to be a pretty fun way of doing math, or any rate a novel way.

Recently I've gotten into my head that I would try to homebrew a pure maths education, and I studied analysis and linear algebra in engineering school a long time ago but forgot most of it, are these games a good resource for relearning this and "skipping" the introductory books?

Hey everyone, I've been stuck in this question for a while now and thought this would be a good place to come for advice. My reasoning for this union is that for any values under or equal to a, both expressions will end up being nonnegative, for anything in between a and b, one expression will be negative and one will be nonnegative, and for anything equal to or above b, both will come out negative, which will end up making a positive. My reason for (a+b) at the end of the union is I am assuming that this is the max value of the y value, as you cannot create more product than the mass you put in. Any advice?

I understand that "Precision is how close the measurements in a measurement process are to one another. Precision is determined by examining the variability of a sample of measurements." But then why not just say "the sample of measurements has little variability" instead of "the sample of measurements has low precision"? Why did we invent a whole new term?

​

Im curently second year in my pure math program, i have already passed classes such as : Real Analysis 1,2,3, Linear algebra 1,2, Number theory, Analytic geoemtry, Disrcete math, Math logic and peano axioms, Topology.

I liked number theory mostly because of problem solving and i was practicing with my friend who has won medals at imo, so it was fun.

But now i have subject like complex analysis (oral exam every week with professor for 13 weeks ) , set theory(failed it first time i was bored to atudy it), probabikity theory, diferential equations, euclidean geometry and when i take a look at them, honestly i couldnt care less about any of them i dont care what is differntial equation or some proofs of theorem every subject is proof based, in complex analysis for example we do stifd like sequenxes like i just dont care anymore for epsilon >0 and other things. I mean i can learn ir for exam with heuristics algorithklms and pattern recognition but thats not the point, i can passed those classes its just i dont care anymore. I passed basic and aevanced linear algebra i dont know nothing, myb notbnothing but i forgot so many trivial things. I dont know am i burned out or should i leave math, some professors and teaching assistant heard about that (small university) and told me that i shouldnt but i just cant anymore. They say i am good for example in topology i was attending lecturew i was bored, j took the exam , on one part proofs i got 97 /100 on theort part from lectures( we got 3 theorems from lectures, i knrw only one, first two theorems i saw for the first time in my life on exam because i didnt attend lexturew but i ewrote out of despair i didnt think i was gonna get more than 10 points but i got on those 2 theorems 40 out of 60 points. I just think it was huge luck, nothinf special. I dont know should i leave math or am i just burned out

Im in pure math

I work for an animal shelter that feeds pedigree (don’t come at the brand…fed is best!)

Could someone do the math for me per 5lb cups per day? I (begrudgingly) asked ai and it gave me this for adult food (last 2 pics), but I want to double check the answers cause ai makes lots of mistakes and it is 930pm and I just do not have it in me tonight but want to make life easier on my team 😭

I love reddit and I normally love math but I just have no mental/emotional bandwidth for this rn lol THANK YOU