Can you prove p → q |- ¬p ∨ q without using the law of the excluded middle or its equivalent? I'm going through a logic book (introductory) and I have an intuition that proving this isn't possible constructively, but I'd like a confirmation.
I'm a computer science major in college. I'm not a freakin' genius, but I do well-- get A's in my classes, good with abstraction (e.g. pointers), etc. However, I seem to have missed... my entire high school pre-Calculus math curriculum? I don't know. [more inside]
I've reached the proverbial straw moment where I'm realizing that, approaching any sort of numbers/critical thinking game or challenge that is meant to be fun, is instead filling me with absolute dread. I find myself becoming incredibly tense and anxious, and very often preemptively angry at myself for OF COURSE being too stupid to pick it up, which means that often I don't even try to pick it up, which then becomes an inescapable feedback loop. I need to change this, please tell me how! [more inside]
I have always been really bad at really simple games, like the ones where there are generally sound mathematical strategies for playing the optimal game. I'd like to compile a little mental rolodex of simple games and their solutions so I can feel smugly superior to any small children who seek to challenge me. [more inside]
Working on a personal project, I am running into a number of math problems of the kind described within. I am not a math expert, so I don't know what to call these kinds of problems, so I don't know how to search for information about them. [more inside]
I have recently been introduced to the concept of pseudoreplication as a mistake that people often make when using inferential statistics to evaluate treatment outcomes. My field (evolutionary and conservation biology) makes heavy use of inferential statistics, including techniques that are vulnerable to pseudoreplication, yet nowhere in my formal education have I been taught about how poor experimental design and lack of statistical rigor can lead to fallacies like this. My personal statistical proficiency is poor, but I am working to remedy that. To that end, could folks help me by identifying and ideally explaining whatever other potential pitfalls you can think of, and explaining how they can be avoided through careful experimental design and data-analysis?
Help me understand this. Math/logic puzzle follows... [more inside]
Are there an infinite number of 2D shapes? [more inside]
I'm trying to express my love for a certain dessert in a math/logic formula. I have this: π > ∼π , which I take to mean "Pi is greater than not Pi", and this: π > ∞-π, which I take to mean "Pi is greater than Everything but Pi". Do these make any sense or hold up in any legit way?
I have a learning disability (dyscalculia/mathematics disorder). Could I handle the formal language component of an undergrad Introduction to Logic class? [more inside]
What is the next step of this Kenken? [more inside]
I am looking for a math typesetting style guide. By this I don't mean the kind of stylesheet for journal submissions that says "Be sure to use the blah-blah-blah LaTeX package and the XYZ equation environment, and our army of editorial assistants will tie up the loose ends and knock off the rough edges." (Why not? Because my advisor is involved in starting a new journal, and suddenly my labmates and I are that army of editorial assistants.) [more inside]
∃x∀y∃z[Qx∧(My→Pyx)∧Wz ∧Pzx] ∨ ∃x[Qx∧∀y(My→Pyx)∧∃z(Wz∧Pzx)] ? [more inside]
I recently ran across a wonderful logic puzzle, but no solution was provided. I eventually worked out a complete solution myself, but it was rather ugly, and I would like to see if people smarter than me can come up with something more elegant. Are there any good Internet puzzle discussion forums floating around? [more inside]
If a man’s wit be wandering, let him post a question about mathematics and reasoning to MetaFilter. [more inside]
Is there a symbol for the phrase "and/or"? [more inside]
math-and-logic-filter: only two more floors - I'm almost there! or am I? [more inside]
Help my friend schedule his bocce leauge: 8 bocce ball teams meet weekly, playing 8 games a week over 4 timeslots (7pm, 8pm, 9pm, 10pm) in 2 courts (courts E and W). [more inside]
I've read that Gödel's incompleteness theorem shows that there are definite limits to what logic, mathematics and by extension computers can do. This seems to be unknown among humanists such as myself. What are the things logic cannot do? Earlier AskMe questions about Gödel here and here (this answer is especially good).