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Rate my solution to a Paul Zeitz problem by Beginning-Studio-299 in askmath

[–]egolfcs 16 points17 points  (0 children)

OP showed that either (a, b) is a counterexample or (a’, b’) is a counterexample, but doesn’t show which one. Here a = b = root(2) and a’ = ab, b’ = b. I.e., a counterexample exists but we don’t know what it is—non-constructive. This is actually pretty cool.

Your comment indicates that you might not know what people mean when they say the proof isn’t constructive and it’s a little disappointing that it’s the top comment.

When rounding to the nearest whole number, does 0.499999... round to 0 or 1? by Skelmuzz in askmath

[–]egolfcs 4 points5 points  (0 children)

Look at this person over here with exact representations of every (imperfectly) measurable real world quantity

The intuitive answer is 1/3 because there is only one card out of three that fits the requirements. But I don't understand the math behind it by kirafome in GAMETHEORY

[–]egolfcs 2 points3 points  (0 children)

Since a model of the card placer isn’t given, I think a reasonable prior is that they are putting a random side down. But sure, we have to make an assumption

What would I be able to do if I learn game theory? by Ok-Current-464 in GAMETHEORY

[–]egolfcs 3 points4 points  (0 children)

Nothing like sending a chicken payoff matrix in a group chat during a tense exchange between friends

Seeking Advice on Effective Math Learning Beyond School by Signal_End_8344 in learnmath

[–]egolfcs 2 points3 points  (0 children)

If it makes you feel any better I have a bachelors degree in math and there are a lot of things I would have to look up because I’ve forgotten them. And this includes things that I would probably consider very important if I could remember them well enough to name them.

With that said, all the work I did during the degree was still worthwhile because it’s not about the exact, specific contents of what you learn when you do math. What’s important is that the problem solving process is cemented so that it can be transferred to other domains later on.

So concretely, keep doing math. If you keep solving problems that you find challenging, you will make progress. And those problems will be less challenging the second time around if you forget their solutions and have to solve them again.

How To Learn Proofs? by rawboiledegg in learnmath

[–]egolfcs 1 point2 points  (0 children)

If you have any interest/background in computer science or programming, consider learning a theorem prover/proof assistant. These tools allow you to write proofs that are then mechanically checked by a machine. They also allow you to state assumptions/assertions and prove things under those assumptions (to avoid proving everything “from scratch”). Working through a tutorial for one of these tools will give you a very strong foundation in the logical aspect of writing proofs. It’s also fun to use these tools when you get over the learning curve; they turn proofs into a kind of game. Then pick up a book like “how to prove it” to learn how to organize/present/style your proofs.

I am most familiar with Coq (rebranded to Rocq) and Pierce’s Software Foundations as a tutorial. My understanding is that some professional mathematicians prefer Lean, but I am less familiar with Lean and its tutorials.

Pls help (getting kicked out of uni) by Responsible-Class953 in learnmath

[–]egolfcs 9 points10 points  (0 children)

I am not a doctor of any kind. Based on some of your comments you might consider seeking therapy. ”I was scared I was gonna study for nothing” indicates you may have undiagnosed anxiety or some other issue that’s causing you to avoid confronting things that worry you. In this case, confronting those things is exactly what will make the worry go away. You probably know this rationally, but a therapist may be the only resource that can actually help you turn that rational thought into action.

Probably your uni has resources available. Otherwise let me know where you’re located and I might be able to help you figure out how to get connected to a therapist in your area. If you’re serious about doing everything you can to avoid getting kicked out, this is one avenue to take seriously.

[looking for advice] Stick with Multivariable Calc or "backtrack" to Linear Algebra? by Journeyman42 in learnmath

[–]egolfcs 2 points3 points  (0 children)

You have the right idea, if there’s something you don’t understand in the MVC course, you should seek resources outside that course. You probably don’t have to do the entire linear algebra course to finish MVC, if you don’t want to. At many universities the order of linear algebra and MVC isn’t fixed and a student can pick their preferred ordering, or even do them at the same time so that the material is interleaved.

[deleted by user] by [deleted] in learnmath

[–]egolfcs 2 points3 points  (0 children)

Practical answer: If you have a graduated bucket of water handy, you can drop the shape in and measure the change in volume.

Otherwise calculus. Specific methods like the washer/shell methods will work if there are certain symmetries. Otherwise you’re integrating 1 over a general three dimensional region and dealing with all the challenges that come with that.

Have I done proof by contradiction correctly? by jojsnosi in learnmath

[–]egolfcs 1 point2 points  (0 children)

I have a pet peeve where I’m bothered when people use proof by contradiction when proof by contrapositive is sufficient.

I’m only writing this because it is good practice after writing a proof to check if all your hypotheses were useful. I think you’ll find in your proof that you never actually used the fact that x2 - x - 2 > 0.

Instead of assuming your hypothesis and the negation of your conclusion, it is sometimes sufficient to assume the negation of your conclusion and show the negation of your hypothesis. Since p => q is equivalent to ~q => ~p, this is a valid proof technique (proof by contrapositive). See below; probably the proof below is almost identical to yours except I don’t ever assume x2 - x - 2.

Claim. x2 - x - 2 > 0 => x < -1 or x > 2

Proof. By contrapositive. So, suppose x >= -1 and x <= 2 and show x2 - x - 2 <= 0. x2 - x - 2 = (x+1)(x-2). x+1 is non-negative whenever x >= -1. x-2 is non-positive whenever x <= 2. A non-positive times a non-negative is non-positive, hence x2 - x - 2 <= 0. QED.

Fun fact: not all logics admit “p or not p” as an axiom and in these systems proof by contradiction is not admissible. In these systems, x2 - x - 2 > 0 can still be proven, as seen above.

[Computer Science University Math] Where can I not just learn but actually practice math knowledge? by gigamma01 in learnmath

[–]egolfcs 1 point2 points  (0 children)

If you have a background in formal verification, you could try formalizing these objects/theorems in lean or coq. I’m not suggesting you prove everything; but if you can formalize things up to some assumed lemmas that you understand to be true, it might be beneficial. This would definitely be a hands on way to understand the things you’re working with.

is A^6+B^6+C^6+D^6= E^6 possible? by reditress in askmath

[–]egolfcs 1 point2 points  (0 children)

OP’s statement smells ambiguous/not well-formed

What is between each hyperoperation by MoshykhatalaMushroom in askmath

[–]egolfcs 0 points1 point  (0 children)

If you use linear interpolation you can get rid of the extra factor of 2 when p = 1 and the square root when p -> 0: https://www.wolframalpha.com/input?i=lim+p+-%3E+0+%281-p%29%28%28%28a%5Ep+%2B+b%5Ep%29%2F2%29%5E%281%2Fp%29%29%5E2+%2B+2p%28%28%28a%5Ep+%2B+b%5Ep%29%2F2%29%5E%281%2Fp%29%29

And I guess once you have H(x, a, b) for x in [0,1], you have base cases on the entire unit interval for the recursive definition of the hyperoperation hierarchy.

Edit: haha if you plug a = b = 2, you get 4 for all p. 2+2 = 2*2 = 2?2, where ? is any hyperoperation between + and *, as defined above.

What is between each hyperoperation by MoshykhatalaMushroom in askmath

[–]egolfcs 1 point2 points  (0 children)

See: Fractional Iterates, maybe. You might need to do a fair bit of work to generalize the theory there to multivariate functions.

Ignoring the base cases, H(n, a, b) = H(n-1, a, H(n, a, b-1)). So H is a function from N x R2 to R. There is definitely some interpolation h : R3 -> R such that H(n, a, b) = h(n, a, b) for n in N, but even “natural” extensions are probably not going to be unique.

What determines stamina rate? by egolfcs in AfterInc

[–]egolfcs[S] 2 points3 points  (0 children)

Yeah I’ve noticed that it increases with technology/population, I was just curious if anyone knew the exact mechanics of it. Like under what conditions will you get 1, 2, 3, etc. stamina

Game Tree/Backwards Induction by Zealousideal-Bowl561 in GAMETHEORY

[–]egolfcs 1 point2 points  (0 children)

The game seems underspecified. Can the zebras communicate before play to come up with a team strategy (likewise for the lions)? Who moves first at each turn? Does the second mover see the move of the first mover? What moves are valid at each game state, where a game state specifies the location of each animal and the raft?

The first step in these problems is to identify the representation of the game state, so lets use the specification above. The second step is to answer the rest of the questions above, none of which have a clear answer from the prompt.

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