Here are the final drafts of the “Group Process Papers.” Assessment details will be distributed in class. Great work, everyone!
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- OpenLab #1: Advice from the Past – 2019 Fall – MAT 2071 Proofs and Logic – Reitz on OpenLab #7: Advice for the Future
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Logic on Math StackExchange
- Optimal Stopping Problem with Perfect Logicians March 29, 2024Question: There is a game that involves $n$ ordered boxes each with a hidden value associated with it. The value is sampled from a probability distribution density function $P(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2}x^2}$. You observe each box’s value in order from box 1 to $n$. After observing any given box’s value, you must decide to pick […]user1306253
- Finding the loop invariant in Hoare logic [closed] March 28, 2024Answer In order to verify that the loop variant holds, we must check that it is strong enough together with the negation of the boolean guard to imply the post condition. Check. It is weak enough to be implied by the precondition. That I cannot verify $y\geq0$ don't directly imply $z = x\dot a$. Can […]Need_MathHelp
- Is $\exists y\forall x(Pxy\land Qy)$ always false? [closed] March 28, 2024Is $\exists y\forall x(Pxy\land Qy)$ always false? I ask because of the following: Let the domain of discourse be the set where x and y are natural numbers and y is always greater than x. Let P be the set of Prime Numbers $\exists x\exists y\left(y>x\land y\in P\right)\rightarrow\exists y\forall x\left(y>x\rightarrow y\in P\right)$ is valid. Also, […]AUTIST INC
- How are existential quantifiers present in the internal logic of regular categories? March 28, 2024Intuitively speaking, how do existential quantifiers appear? I'm just starting to get familiar with these definitions. Top and conjunctions appear because of finite products. (Plus, I assume, something that makes them work nicely with the existential quantifiers.) But my understanding of existential quantifiers in categorical terms is by way of them being left adjoint to […]Julián
- Introducing function symbols in (first-order) set theory March 28, 2024Suppose we want to formalise some parts of mathematics within set theory, which is itself formalised in a first-order language (in the standard way). Logic is assumed to be classical. In particular, this means that – at the level of semantics – every term must have a denotation, which in turn means that every function […]wiktoria
- Question regarding the completeness theorem and ZFC March 28, 2024In order to prove the completeness theorem we obviously need a framework such as ZFC (I'm aware that ZFC isn't the only possibility) so that we can talk about a language $\mathcal{L}$ and also about models of $\mathcal{L}$. Now the completeness theorem makes perfect sense to me in so far as the language which we […]Gergő Kelemen
- How to translate this statement into $A \land B$? March 28, 2024A friend of mine showed me an SAT question today in which one of the choices is: No genetic variations that were common to those finches that used technique Q were not common to the finches that did not use technique Q. I just learned a bit about logic so I tried breaking down the […]ten_to_tenth
- Referencing a statement with quantifiers in two separate lines March 27, 2024I want to show that a statement with several quantifiers, e.g., "$f(a, b)Ruth
- What is the matter in defining the necessity operator internally $\Box: \Omega \to \Omega$? March 27, 2024I am looking for ways to internalize the modal operator of necessity $\Box$, ending up with a morphism $\Box: \Omega \to \Omega$ satisfying the necessitation rule (if $\phi$, then $\Box \phi$) and the distributive under implication $(\Box(\phi \to \psi)\to (\Box \phi \to \Box \psi))$. The reason why is I would like to study categories in […]Miviska
- Topological properties vs homeomorphisms March 27, 2024I'm studying general topology and a question has come to my mind. We have defined a topological property to be a property which a (viz. any) topological space can satisfy or not satisfy, and such that, if satisfied by a space, is also satisfied by every space homeomorphic to it. I can see the ambiguity […]Amanda Wealth
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