If I was invited to give advice to entering students on the first day of Mat 2071 I would tell the students to always be prepare for class, and pay attention to the teacher when he or she is explaining the course. I would tell them to come in class at time, and do not miss a lot of days in order for them to keep in track. I would also advise them to always ask questions when they don’t understand something, and keep practicing the subject in class and also at home which would help them to progress and also succeed in the subject.
Logic on Math StackExchange
- "You cannot engage in argument unless you rely on the principle of non-contradiction" December 9, 2024A very good SEoP article "Aristotle on Non-contradiction" by Paula Gottlieb makes two interesting claims, one after the other: Claim 1: "Anyone asking for a deductive argument for PNC [the principle of non-contradiction], as Aristotle points out, is missing the point, or, rather, is asking for something that is impossible without using PNC." Claim 2. […]logiclearner
- Why does "p⊃q" instead of "q⊃p" mean "if p then q"? [closed] December 9, 2024The “if-then” sentence is called a conditional and will be symbolized as (p ⊃ q). The part to the left of the horseshoe is called the antecedent (what comes before), and the part to the right of the horseshoe is called the consequent (what comes after). So why does "p⊃q" instead of "q⊃p" mean "if […]陈海斌
- Do we need not need truth values to describe models in predicate logic? December 8, 2024I am reading Kirby's Model theory. In section 3.3, the following definition of interpretation is given: $\textbf{Definition 3.4 (Interpretation of formulas)}$ Let $\varphi$ be a formula of $L$ and $\bar{x} = (x_1, \dots, x_n)$ a list of variables containing every free variable of $\varphi$. We also write $\varphi(\bar{x})$ for the formula with the list of […]Brian
- Can proof by contradiction be used disprove a statement? December 8, 2024I'm currently taking an introductory proofs class. The textbook that we are using justifies proof by contradiction by stating that the statement $P$ is logically equivalent to the statement $(\neg P\implies(Q\land\neg Q)).$ The logic makes sense to me when we use the proof technique conventionally as follows: assume that $\neg P$ is true and then […]Learning Math
- Show law of excluded middle is valid December 7, 2024Example 1.12 from David Marker's An Invitation to Mathematical Logic (p. 10) shows $(\phi \vee \neg \phi)$ (that is, the law of excluded middle (LEM)) is valid in finitary model-theoretic FOL: For any $\mathcal{L}$-structure $\mathcal{M}$ and any assignment $\sigma: V \rightarrow M$, $$\mathcal{M} \models_\sigma \neg \phi \Leftrightarrow \mathcal{M} \not\models_\sigma \phi $$ Thus $\mathcal{M} \models \phi$ […]silly-little-guy
- How do you construct a While loop using propositional dynamic logic? December 7, 2024I am learning some modal logic from a textbook (Modal Logic from Blackburn, De Rijke and Venema) and they have an example about propositional dynamic logic (PDL). Here they explain that if $\pi$ is a program, then $\pi^*$ is also a program, and $\pi^*$ is an iteration of $\pi$ for a finite (possibly zero) number […]UnrulyTank
- Proof of Deduction Theorem in Hilbert-Calculus, Beginner friendly December 7, 2024Deduction Theorem: Let $ \Sigma$ be an axiom system, and let $ \psi, \varphi$ be $ L$-formulas. Then the following always holds: $ \Sigma, \psi \vdash \varphi \iff \Sigma \vdash \psi \rightarrow \varphi $ “$ \Rightarrow$” We prove by strong induction on the length of a proof $ n \geq 1$ that for arbitrary $ […]God
- Proof of the General Deduction Theorem December 6, 2024Theorem: For all axiom systems $\Sigma$ and all formulas $\varphi, \psi_1, \ldots, \psi_n$, it holds that: $ \Sigma, \psi_1, \ldots, \psi_n \vdash \varphi \iff \Sigma \vdash \psi_1 \to \ldots \to \psi_n \to \varphi$ Proof: $\Rightarrow$: We prove by complete induction. Initially, that is, for $n = 1$, it holds: Let $\Sigma, \psi_1 \vdash \varphi$, and […]God
- Do "truly" infinite proofs exist? December 6, 2024An assumption underlying this earlier question was the existence (and greater expressive strength) of infinite proofs in logics like $\mathcal{L}_{\omega_{1}^{CK}, \omega}$ (based on, for example, the discussion in §2 chap. IX of Mathematical Logic by Ebbinghaus et. al., and answers like this and this) However the comments in response to the question have led me […]NikS
- How do you define universal and existential quantification rigorously and non-circularly? December 5, 2024Universal and existential quantification are necessary to build math from set theory. But I can't think of any way to define them besides the traditional intuition: that is, $(\forall x\in S)[p(x)]$ means "for all $x$ in $S, p(x)$" and $(\exists x\in S)[p(x)]$ means "there is some $x$ in $S$ such that $p(x)$". I know that […]Mathemagician314
Hi Miralia,
Thanks for the response – that’s great. I’d prefer that you leave it as a comment on the OpenLab #1 assignment, here:
https://openlab.citytech.cuny.edu/2017-fall-mat-2071-reitz/?p=292
(scroll to the bottom and you’ll see that you can leave a reply – just copy/paste it in there). This will ensure that it gets counted correctly for your grade.
Best,
Prof. Reitz