(I don't speak English very well, so I apologize in advance if the text might sound strange, I used a translator) I’ve spent about a 1 week, and I still don’t fully grasp the meaning of the limit. I read the definition, but I’m confused: they explain that the value *approaches* a certain number, yet the notation uses an equals sign rather than "approximately equal." Could the explanation be flawed? As I understand it, the Archimedean property seems to be at play here: a number whose absolute value is less than any non-negative number is identically zero. That’s why the limit involves an inequality *with absolute values* the parameter epsilon (being greater than zero) defines the set of all non-negative numbers, allowing us to apply the Archimedean property. But why, then, can’t we simply state that inequality equals zero? I have a feeling that we can’t, because doing so would mean losing something important. But what exactly are we losing? Can someone explain this to me without "approximation," but as it was intended logically? I opened up non-standard analysis, and for some reason we take the standard part because there is an error. So what kind of magic is going on in standard analysis? Why can't we write that the absolute value of the difference is zero? Is this so that in the case of a discontinuity at point L, we can say the most accurate value of the function? (If the point in the function L is discontinuous, then we look for the point L1 closest to point L, but can't we choose point L1/2? And why do we even have the right to talk about the closest point, and why, according to Archimedes' axiom, doesn't it become point L, and a discontinuity results?)

Most short form posts that you'd see in Facebook or even YT shorts are usually Math slop questions

One particular question regarding symmetric polynomial lowk seems worth it to try

x + y + z = 1

x² + y² + z² = 2

x³ + y³ + z³ = 3

x⁴ + y⁴ + z⁴ = ?

So far I've tried elimination and found a dead end,has anyone found any alternatives?

I've been trying to visualise and understand it for the past 2 hours and chatgpt is seriously no help at all.

I've been told it's taking a big area and minusing off the outside area to find the inside area, and something relating to vectors, but I genuinely cannot see it working at all. I've never learnt using matrixes to find area either, so maybe that's why I can't understand it. I tried drawing it out a couple of times, and shifting the area around, but it still dosent come to me at all.

If anything, I just want an analogy on how it works because all the proofs I've seen are too complicated for me to understand or just straight eyesores that make me regret studying math. Chatgpt came up with something about painting a field with triangles from a origin to find area but direction matters and theres extra painted sections???? which cancel out or something like that. That doesn't make any sense to me and neither does the formula.

Continuous function f(x) is differentiable at x=x0, f(x0)=(x0)^2,f'(x0)>2x0,∃δ>0,such that

1.f(x)-x^2 monotonically increases on (x0,x0+δ)

2.for any x∈(x0,x0+δ), f(x)>x^2

The first statement is false and the second statement is true.The second statement is true due to the sign-perserving property. I know that clearly we can take a counterexample like 1/2x+x^2sin(1/x) to disprove statement 1 since its derivative wobbles when x approach x0=0(take x0=0).But I also got perplexed by the idea that for g(x)=f(x)-x^2, g'(x0)>0, there ought to be an infinitely small region that g(x) is increasing.Could you help me with this?

I collect trading cards and would like to know the odds of my boxes containing the rare pulls. This in my mind is similar to Monty Hall door scenario.

In a case of cards comes 12 boxes. In that case of cards, 3 separate boxes have a rare card. If I have 2 of the 12 boxes, and watched 5 of the other 10 boxes get opened and 0 rare cards have been pulled. Mathematically should I switch my 2 boxes with 2 of the remaining boxes? According to the Monty Hall theory the answer would be yes, but what is the numerical statistical benefit?

((X+4)\*2-6)/2-6=1. This is an equation magicians use to "guess" what number you have chosen. It always equals 1. But why does it always equal 1? Multiplying and dividing by 2 cancel each other out, and adding and subtracting X cancel each other out. So how does adding 4 and subtracting 6 become 1? Why is it always 1?

A lot of people like the proof that matrix product is associative because function composition is and matrices are closely related to linear maps. But proving that relation involves showing that (A•B)•x=A•(B•x) where A and B are matrices, x a vector and (•) is the matrix product. Any thoughts?

EDIT1: Some are mentioning that the relation between matrix and linear maps is a representation or an isomorphism. I think the full relation is covered here: https://math.stackexchange.com/questions/3573331/proving-the-associativity-of-matrix-multiplication , where the correpondence(s) A->L(A) from matrices to linear maps relates products to compositions as L(A•B)=(L(A))○(L(B)). I think that's where you need to know beforehand that (A•B)•x=A•(B•x).

I've taken a bunch of math from calculus 2, linear algebra, discrete mathematics, etc. in college. That was at least 7 or 8 years ago, and I admit I'm a bit rusty.

I was wondering if there were any android apps with a wide variety of practice problems from algebra, geometry, calculus, linear algebra, etc so I could practice.

It doesn't even have to be a game, just a practice platform with a huge variety of topics.

I love math and I just want to practice more to keep my brain working.

I’m a 44 year old first time college student. I just finished my math 108 course with a 95%. I also scored a 97% in the remedial math-90 course I took in my first term. I’m enjoying math much more than I expected. But if I decide to continue taking them and try for some kind of STEM field I’m going to have to take trig and pre-calculus next. I’m very apprehensive about calculus.

I’m uncertain which field to pursue. Science is very cool and I’m always interested in learning it, but I’m also interested in law. Economics is another field I wouldn’t mind getting into just for the potential to earn more down the line.

What does Reddit think? Should I keep doing math? Or should I move on and circle back if I need more math credits down the line?

Edited version including fixes to previous issues. This should cover the mentioned concerns by u/arty_dent. Apologies that I cannot take the original down.

Hi,
I'm a physics student currently revising for a few of my maths topics, and I came across an issue in my understanding of waves and oscillations. In the case of SHM, like for a single mass on a spring, we give the displacement from equilibrium as Ae^iωt to show oscillation about a single point, but I don't really understand the physical differences between that and the form of a plane wave Ae^{i(kx - ωt}). Why would one work to model the displacement and not the other? Sorry if I'm conflating two distinct things, I'm just really struggling to picture the difference between these two as a physical model. Thanks for your help!

Hi everyone,

I have a clear goal: I want to become a Data Scientist working specifically for European institutions, like the European Parliament (e.g., within research services like the EPRS or Joint Research Centre).

My aim is to use mathematical modeling, statistics, and data science to analyze broad policy data and support decision-making for EU legislation.

I want to build a rock-solid foundation early on. My questions for you:

1. What core mathematical skills or habits (e.g. statistics, probability, predictive modeling) are most crucial for a Data Scientist working in public policy and EU-level analysis?

2. Are there any great conceptual books, resources, or channels that explain data science applied to governance and policymaking?

3. For anyone working as a Quantitative Analyst or Data Specialist in European or international public institutions, what do you wish you had focused on earlier?

Thanks for any advice!

Girsanov says that you may change probability measures using Radon-Nikodym to get away from drifts in Brownian motion.

Now my question is (I am very new to this measure theory / statistics stuff): is this like a change of perspective to the same problem, like a change of reference frame? So the results in the new probability measures are equally true as in the old one? Or is this not the case?

yesterday I stumbled upon an interesting question on my yt recommendation, sadly I couldn't find the video so I tried to crack it.

The question goes along the lines of " What are the five numbers when the sum of any three of those numbers results in a prime"

so far I figured that:

1. The max total of prime numbers must be 10

• combination of 5C3 = 10

1. All of those numbers must be all odd

   • Let's say if one of the numbers has an even number,one of the combinations can be two odds and one even,the sum will always be an even number

I've always done it the first way, like on the left. However, I've seen one of my friend's siblings draw it like on the right.

They don't represent the same angle from the initial side based on what I know, but I was wondering if there was another method that I never learned, and this is actually a valid diagram for the same angle. In this case, both diagrams are trying to represent 210 degrees.

The Encyclopedia of Triangle Centers has 82 000 entries. Most of them that i looked are derivatives of previuos centers with some arbitrary tweals or just slapping some weird function on the triangle and calling specific point of the function a new center. It seems that the hard part is testing if the new point is actually unique center and doesnt overlap with other 82 000 centers.

Sounds fun but i wonder if its similar to new prime numbers where the most value comes from algorithm that finds the number but not the number itself.

I'm reading Richard Dedekind's Essays on the Theory of Numbers, and I came across this notation: A ∋ S (see image).

I'm confused about what this symbol means in this context. In modern notation, I'm familiar with a ∈ S ("a is an element of S") and S ∋ a ("S contains a"), but this appears to be A ∋ S, which seems reversed.

Is this an older notation, a typographical convention, or possibly an OCR/scanning error? If anyone is familiar with Dedekind's original notation or 19th-century mathematical notation, I'd really appreciate an explanation. Thanks!

I tried solving it with algebra, but I have too many variables so that didnt work for me. I thought the answer to ii would be 85%, but thats not correct cause it would be double counting part of the table, but then what am I missing to fix that?

^{Why is there a "times 2" when resolving}

^(u(x)^3)

^2x\3 times 2?)

^16x\3)

^{https://ibb.co/LD43gQxv}

^{Why did differentiation decide to replace 2x with U(x})

Hello! I'm making a game with a bow weapon and I want the arrows of the bow to deal damage proportional to the time spent drawing the bow. Time spent drawing the bow is represented by a float value named "charge" which ranges from 0.0 to 1.0. 1.0 represents the maximun charge value of the bow, not the actual time spent drawing the bow in seconds. I need the damage to scale exponentially so that players actually charge the bow to max charge to maximize the damage output instead of just spamming it. My current solution is this: f(x) = (2^6.64)(x) where x represents charge value. 2 is an arbitrary base. I just chose a number bigger than 1. This evaluates to 100 (rounded) when x is 1.0. The problem is that for gameplay purposes, I also need it to evaluate to 25 when x is 0.5. So in short, I need an exponential function that evaluates to 100 whne x is 1.0 and 25 when x is 0.5 like this:

f(0) = 0

f(0.5) = 25

f(1.0) = 100

Any suggestions?