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    [–] As seen at BYU. #facepalm HarryPotter5777 3 points ago in math

    Polite criticism of viewpoints and posts about mathematics which relate to politicized topics are acceptable. Unsubstantiated accusations of sexism and strawmanning are not. No one in this thread has said anything resembling the statements you've accused them of. This is your final warning to act in good faith in this thread.

    [–] As seen at BYU. #facepalm HarryPotter5777 6 points ago in math

    Your comments are edging dangerously close to violating our rules against general political debate and overall impoliteness; if you're going to continue this conversation, please keep it more civil and mathematics-specific than you've been doing so far.

    [–] sorry, please don't ban me HarryPotter5777 1 points ago in math

    See here for a formal definition of P vs NP; a language is a specific set of strings in the language. A language is in P if there is a polynomial-time (polynomial in the length of the input) algorithm which can decide for all input strings whether that string is in the language.

    But again, I suggest that you change your goal from "prove P≠NP" to "get a better understanding of P vs NP and some other topics in theoretical computer science" - the idea of a language is essential to the definition of the problem, so it would be rather implausible that a valid solution exists without even making use of the concept.

    [–] sorry, please don't ban me HarryPotter5777 1 points ago in math

    What do you mean by a binary system? That's not standard terminology anywhere, to the the best of my (or Wolfram Mathworld's) knowledge. Base-2 representation, perhaps?

    What do you mean by "M's solution"? You have to define these things rigorously, and Turing machines are not generally understood to have solutions any more than potatoes are.

    What variables are not defined before they are used?

    B and D, for one. I assume you meant something like "let B be an arbitrary subset of E", but if so you need to say that - just writing down symbols like that doesn't distinguish it from "B, which was defined above, is a subset of E" or something else.

    You 'define' M as "M ∈ deterministic Turing machine" but "deterministic Turing machine" is not a well-defined set for you to choose an element of. If you mean "Let M be a deterministic Turing machine", or "M is defined as the following specific deterministic Turing machine", you again need to say this, and you don't need to include (and indeed should omit) the ∈ symbol to make that coherent.

    [–] sorry, please don't ban me HarryPotter5777 1 points ago * (lasted edited 7 hours ago) in math


    |B| is an integer, w is a binary string. Integers are not in general divided by strings.

    M class NP

    I'm not sure what this trying to say, but it isn't saying it correctly. NP is a class of decision problems, not Turing machines.

    Throughout the proof you use very strange symbolic notation to the exclusion of almost any verbal elaboration, and you don't do so in any standardized sense, which leads to things like throwing in variables before you've explained what they are. Having more symbols doesn't make a proof more correct, and when they're not used in standardized ways it just makes trying to work out what the author might have intended an enormous hassle.

    For instance:

    M solves PROBLEM

    There are a number of things this could mean. "Let M be a Turing machine such which decides the language PROBLEM (not that PROBLEM seems to have been defined as a language)"? "We claim that M, which was previously defined, decides PROBLEM"? Something else entirely? Nearly every line in the post is like this, and it makes it nigh-impossble to figure what you meant in the first place.

    [–] y=2(3x)^3+5 Transformation HarryPotter5777 1 points ago in math

    From the sidebar:

    Homework problems, practice problems, and similar questions should be directed to /r/learnmath, /r/homeworkhelp or /r/cheatatmathhomework. Do not ask or answer this type of question in /r/math.

    [–] sorry, please don't ban me HarryPotter5777 1 points ago * (lasted edited 8 hours ago) in math

    It looks like you're trying to provide a Turing machine M which computes the solution to a problem in NP in greater than polynomial time. That's not sufficient to resolve P vs NP; to do that you'd need to show every such Turing machine took greater-than-polynomial time to resolve your chosen decision problem. It'd be like trying to prove Fermat's Last Theorem by observing that 175+625≠35 - you've got ∞ more cases to go before you finish.

    If you want to investigate a mathematical phenomenon, that's great and should be encouraged, but frankly your chances of resolving P vs NP are incredibly slim even if you had a PhD and 3 decades' work on the problem; claiming a proof (one that fits in a short reddit post, at that!) with past failures and a lack of recognition of the sheer amount of work that has gone into the problem already comes across rather poorly to most people.

    [–] Is this game possible to beat? (inspired by Conway's Soldiers) HarryPotter5777 3 points ago in math

    I don't know about in every case, but it's certainly possible to win this game in some cases. The trick is instead of trying configurations and solving them, work backwards - start with a single filled tile, and 'anti-jump' adding tiles until you can make 25 initial ones. (Just playing around with it a bit, I found a viable one with 32 initial tiles - I wouldn't be surprised if 35 were possible.)

    [–] Is this game possible to beat? (inspired by Conway's Soldiers) HarryPotter5777 8 points ago in math

    Few people are going to want to download and run mysterious .exe files, and many people won't be able to; can you describe the rules of the game?

    [–] Carat Conundrum HarryPotter5777 1 points ago in mathriddles

    Alternate solution:

    Given a real-valued solution, we have some parition of the other numbers for each removal; this generates a series of linear equations with rational coefficients, so if a solution exists one can find such a solution with rational values (including the non-uniform one, if any such exist). Then we can turn that into a statement about integers. Since the property is translation-invariant, we can set these integers up so that one of them is 0. Parity concerns show that all of the other integers must be even; then it is possible to divide by 2 and obtain a smaller solution. By infinite descent, it follows that no solution can exist with all entires nonzero.

    [–] Has there ever been a case of an incorrect proof being thought to be correct? HarryPotter5777 45 points ago in math

    In 1879, Alfred Kempe claimed a proof of the 4-color theorem, and it took over a decade for anyone to notice something was wrong with it; I think you can find a modern-worded version of the proof somewhere, and it's a fun exercise to try and find the mistake.

    [–] Figuring out between which consecutive numbers the root lies? HarryPotter5777 2 points ago in learnmath

    6 = √36, and 7 = √49. Since the square root function is increasing, √46 is going to be in between those two numbers, so it'll be between 6 and 7. Does it make sense how to extend that to the other examples?

    [–] Comic 3683: By Court Order HarryPotter5777 14 points ago in questionablecontent

    Surprisingly, no! I just went through all the Yelling Bird comics and this one is the closest with a total of 11 curses (runner-up had 8, I think).

    [–] How do I estimate where the root of a number lies? HarryPotter5777 1 points ago in math

    From the sidebar:

    Homework problems, practice problems, and similar questions should be directed to /r/learnmath, /r/homeworkhelp or /r/cheatatmathhomework. Do not ask or answer this type of question in /r/math.

    [–] Math HW in LaTeX? HarryPotter5777 26 points ago * (lasted edited a day ago) in math

    Undergrad here, been doing all my assignments in LaTeX since I arrived. LaTeX definitely does take some time to figure out, and the learning curve is steep; that said, once you do have the basics down it can be quicker, especially if it takes a fair bit of effort already for you to produce legible proofs.

    Here's a really basic example of a template for a homework assignment that demonstrates some basic functionality:

    \geometry{a4paper} % or letter or a5paper or ... etc
    \title{Classname Homework 1}
    \author{Firstname Lastname}
    %\date{} % delete this line to display the current date
    \noindent \textbf{Section 1.2.3}
        \item [3.] Prove that the function $f: \mathbb{N} \to \mathbb{Q}$ given by $f(n)=\frac{n}{2}$ is injective.
        \item [7.] Compute $1^2+2-3$.
        \item [9.] 
            \item Show that the number of ways you can choose a 3-element subset of a 5-element set is ${5\choose 3}=10$.
            \item Consider the following display-style equation:
            \[\sum_{n=1}^\infty n^{-n} = \int_0^1 x^{-x}\, dx\]
            \item Define the derivative $f'(x)$ of a function $f$ at a point $x$ as 
            \[\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}\]

    You can either install something natively on your computer, or use a number of online resources for doing LaTeX - ShareLaTeX and Overleaf are the two main ones. As always, Google is your friend for any command you might want to learn. Detexify is your friend for all your symbol-related needs.

    If you put in a few hours playing around with this stuff over a weekend, it shouldn't be hard to get enough of the basics down that you can type up a nice-looking homework assignment without too much trouble.

    [–] Will 115.5 make AIME? (on 10A) HarryPotter5777 1 points ago in math

    Art of Problem Solving is going to be infinitely more helpful than /r/math for this, the vast majority of active commenters here are undergrads at least. Look and see how other people have been doing, throw out a guess for percentile rankings, compare with past years, and you might get a decent estimate, but it's always a little uncertain.

    [–] Proof correct? Union of two disjoint countably infinite sets is countably infinite. HarryPotter5777 2 points ago in math

    I generally try to maximize the amount of time I can spend thinking about the structure of the actual proof and what's on the board, which means minimizing the amount of time it takes me to cover the essential stuff in my notebook; as such, my notes tend to be very dense with a lot of personal shorthands and abbreviations (and omitted proofs in any situation where I expect future-me to be able to derive them without trouble). But I could imagine in a context where I wasn't trying to keep track of several new results and proofs that my notes would be a lot wordier.

    [–] Proof correct? Union of two disjoint countably infinite sets is countably infinite. HarryPotter5777 25 points ago in math

    You haven't defined f, g, h, or N here - it's not at all clear which objects you're talking about, why they exist, or how to construct them.

    [–] Simple Questions HarryPotter5777 3 points ago in math

    Undergrad here who took a lot of advanced courses pre-college: I didn't get credit for them, but after talking to the head of the undergraduate mathematics department I was able to get a lot of those requirements waived and take much more advanced and interesting classes, and the ones I'm retaking now I'm still getting a lot out of because they're at a more in-depth level than what I did before and I'm getting a chance to solidify those concepts - not boring at all.

    [–] Galactic Gold Rush HarryPotter5777 6 points ago * (lasted edited 2 days ago) in mathriddles

    If the deposit is on the surface of the planet, A wins. If it's not, then there are 6 cubes adjacent to it which, if removed, cause the next player to get the gold deposit. Therefore, neither player will take any of these adjacent cubes until there are no others. So it's simply a question of parity of the number of other cubes: when n is even, n3-6-1 is an odd number of cubes to remove, so it will be B who is forced to take a neighboring cube and A who wins, while when n is odd the reverse is true. So A wins all the time when n is even, and B wins with probability (n-2)3/n3 when n is odd (and greater than 1).

    [–] Favorite Integer Constants HarryPotter5777 2 points ago in math

    Whoa, that's awesome! I would not have guessed the answer would be finite.