**Written work, **Due Tuesday, November 7th, in class:

Chapter 9 p152: 3, 4, 5

**WeBWorK **– none

**OpenLab **– OpenLab #7 due Thursday, November 9th

**Project** – Group Process paper initial draft due November 16th

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**Written work, **Due Tuesday, November 7th, in class:

Chapter 9 p152: 3, 4, 5

**WeBWorK **– none

**OpenLab **– OpenLab #7 due Thursday, November 9th

**Project** – Group Process paper initial draft due November 16th

- Defining relations. June 13, 2024Do these answers provide what is required? Even(x)=∃k(x=2*k) Triple(y,x)=∃x(y=3*x)Lior
- Why did Tao include the reflexive axiom for equality here? (Analysis I) June 13, 2024In Analysis I, Tao lists several axioms which equality, defined upon a class of objects $T$, must satisfy. The reflexive axiom he gives is Given any object $x$, we have $x=x$. However, from Wikipedia here, equality between 2 expressions asserts "that the expressions represent the same mathematical object". This makes the reflexive axiom seem superfluous- […]Princess Mia
- Would this logic be considered constructive? June 13, 2024I have asked about similar logics before, but this one is different. The logics that I’ve asked about in the past take the Gödel-McKinsey-Tarski translation for Intuitionistic Propositional Logic to classical $S4$, but change the translation of negation to $t(\neg A)=\neg \Box t(A)$. If you define the translation thus: $t(p)=\Box p$ $t(\neg A)=\neg \Box t(A)$ […]PW_246
- Whats the solution to this mathematical reasoning problem? June 12, 2024A multiple-choice test question offered the following four options relating to a certain statement: A The statement is true if and only if x > 1 B The statement is true if x > 1 C The statement is true if and only if x > 2 D The statement is true if x >2 […]Saqlain Syed
- Does Dan Willard demonstrate that classical logics with the Law of the Excluded Middle versus those with Double Negation Elimination are distinct? June 12, 2024Context: Dan Willard's 2020 review paper of his work on Self-Verifying Theories/Self-Justifying Axiom Systems (SJAS) is titled "How the Law of Excluded Middle Pertains to the Second Incompleteness Theorem and its Boundary-Case Exceptions" [0]. In it, he claims that by disallowing the Law of the Excluded Middle (LEM) as a axiom schema, SJAS of sufficiently […]jpt4
- Justifying a swap from (mathematical) implication to material conditional and whether the antecedent of equivalence operator is assumed to be true June 12, 2024Suppose I would like to prove the Pigeonhole Principle using a Proof by Contradiction. The Pigeonhole Principle states that if s objects are placed in k boxes for $s>k$, then at least one box contains more than one object. In other words, I must prove that: P $\implies$ Q where P denotes the statement s […]bluesky
- In what logic are the results of soundness proven? [duplicate] June 12, 2024When you want to prove that propositional logic, first-order logic, etc. is sound, that is to prove that all deduction rules preserve truth, what is the logic you are working inside? https://www.cs.toronto.edu/~axgao/cs245_f19/slides/lec09_prop_soundness_nosol.pdf Because if you assume that say first-order logic is sound in order to show that proposition logic is sound, then I don't find […]Anserin
- Conventions for expressing nested logical relations June 12, 2024Suppose I want to say that the conditional statement $P\implies Q$ is also equivalent to $(\sim P)\lor Q$. Writing it like this is confusing: $P\implies Q \equiv (\sim P)\lor Q$ I have a few solutions. $``P\implies Q" \equiv ``(\sim P)\lor Q"$ $(P\implies Q) \equiv ((\sim P)\lor Q)$ Let A denote the statement $P\implies Q$ and […]bluesky
- Does $\forall x(x\in B\implies x\in A)$ imply that $((\forall a\in A)P(a)\implies (\forall b\in B)P(b) )$? June 12, 2024I was solving a problem like $$\textrm{if} \:f\in C(A)\:\text{and}\:B\subset A,\: \text{then}\: f|_B\in C(B).$$ I transformed $f\in C(A)$ so $f$ is continuous on A and therefore $$(\forall a\in A)(\forall \epsilon>0)(\exists\delta>0)(\forall x\in A) \quad |x-a|Owen An
- Axiomatization of the theory of finite structures in a signature consisting only of function symbols June 11, 2024The following question is inspired by this question here. In that question, the OP asked whether there is a theory $T$ in the signature of a single binary operation $\{\ast\}$, s.t. $T$ admits both finite and infinite models, and furthermore $T$ is the same as the theory of its finite models. I noted in the […]David Gao

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