Hi everyone,

The answer key for the Final Exam Review Sheet is now complete (it can be found in Classroom Resources / Exam Reviews ).

Regards,

Prof. Reitz

Skip to the content

Hi everyone,

The answer key for the Final Exam Review Sheet is now complete (it can be found in Classroom Resources / Exam Reviews ).

Regards,

Prof. Reitz

- OpenLab #1: Advice from the Past – 2019 Fall – MAT 2071 Proofs and Logic – Reitz on OpenLab #7: Advice for the Future
- Franklin Ajisogun on OpenLab #7: Advice for the Future
- Franklin Ajisogun on OpenLab #3: “Sentences”
- Franklin Ajisogun on OpenLab #6: Proof Journal
- Jessie Coriolan on OpenLab #7: Advice for the Future

- What does it mean that we need $𝜖_0$ induction to prove PA consistency? March 20, 2023I have started to learn about Peano Arithmetic, and also about ordinals. In particular, I have seen that the Goodstein theorem is an example of a statement that can be expressed in PA but that requires other axioms to be proven. In particular, ZFC axioms (or just ZF?) let us construct ordinals up to $𝜖_0$ […]Weier
- Two definitions of $\limsup$ on sequences of sets and underlying logic systems March 20, 2023Let $X$ be a set, $(E_n)$ be a sequence of subsets of $X$. As I know, the definition of $\limsup_n E_n$ is the subset of $X$ consists of $x \in X$ such that $x \in E_n$ for infinitely many $n$. Also, there is a definition using union and intersection: $\limsup_n E_n = \bigcap_{n = 1}^\infty […]cwlo2F
- Is there a sheaf model where the Weak Markov's principle fails? March 19, 2023We define a real number $x$ to be pseudopositive if $\forall y \in \mathbb{R}$ we have $ \neg \neg (y < x) \vee \neg \neg (y > 0) $. The Weak Markov's Principle (WMP) is the axiom that every pseudopositive real number is a positive real number. This clearly follows from the analytic Markovs Principle […]saolof
- How to find latitude and longitude values of point on surface of earth knowing the latitude and longitude values of a point nearby March 19, 2023Assume that there are two points $x_1$ and $x_2$ on the surface of the earth. Assume that we know the distance between both points, and we know the geo-coordinates (longitude and latitude) of $x_1$. So, how can I find the geo-coordinates of $x_2$? I tried to find a solution online, and I read that a […]Techistan pro
- Can Gödel's theorem be proved within PA? March 19, 2023Gödel proves his theorem informally by using natural languages. However, is there a way to carry out his proof in PA itself? (so that maybe PA could prove that itself could not prove its own consistency) If there isn't (and we have to carry out his proof in some stronger background theory such as ZFC), […]Nicholas
- Beginner logic question on the continuum hypothesis March 19, 2023I am very new to logic and don't know very much about it. One thing that I know is that there are models of ZFC in which no cardinal lies strictly between $|\mathbb{Z}|$ and $|\mathbb{R}|$. There are also models of ZFC in which the continuum hypothesis is true. Based on this, we know that ZFC […]Cayley-Hamilton
- Statement is true but contrapositive is false? March 19, 2023It seems that the contrapositive of a true statement is true. Consider the following: $A,B,C,K\in \mathbb{N}$ $\exists A,B,C: A^K+B^K=C^K→K≤2$ Take the contrapositive: $$K>2→∀A,B,C:A^K+B^KC^K$$ However, can the contrapositive of a true statement be false? I ask because of the following: $A,B,C,D,K\in \mathbb{N}$ $\exists A,B,C,D: A^K+B^K+C^K=D^K→K≤2$ Take the contrapositive: $$K>2→∀A,B,C,D:A^K+B^K+C^KD^K$$ But this seems false due to the […]AutistandProud
- "No integers $x$ and $y$ exist for $28x+7y=8$" March 19, 2023What is the logical structure of this statement? No integers $x$ and $y$ exist for $28x+7y=8.$ I'm not sure, but I think the answer is $$¬∃x\;∃y\;(x ∈ \mathbb Z ∧ y ∈ \mathbb Z ∧ 28x + 7y = 8).$$user1161390
- Gödel's second incompleteness theorem and Consistency. March 18, 2023According to Gödel's second incompleteness theorem, no consistent axiomatic system which includes Peano arithmetic can prove its own consistency. As I understand it, this result contributed to spark a crisis in the foundations of mathematics. What I don't really understand is of what use would be proving that a system of axioms is indeed consistent. […]Alessandro
- Every subset of $\Bbb N$ is defineable in the language of monoids March 18, 2023Let $\mathcal L=\{\cdot,e\}$ be the language of monoids so that $\cdot$ represents an operation which is closed and associative, and $e$ represents an identity. Consider the structure of natural numbers on this language. I have proved that every singleton $\{n\}\subseteq \Bbb N$ is definable in this language. I'm now trying to determine whether every subset […]Addem

"Math Improve"
.999
1
assignment
assignments
calculus
calendar
Doodling
exam #3
exam 3 grades
final papers
grading criteria
grading policy
graph theory
group paper
group project
homework
logic
mathography
metacognition
only if
openlab
OpenLab #4: Bridges and Walking Tours
OpenLab7
OpenLab 8
OpenLab8
Open Lab 8
openlab assignment
perfect circle
points
presentation
project
resource
rubric
semester project
spring classes
vi hart
ViHart
visual math
Wau
webwork
week 8
week 14
welcome
written work

© 2023 2018 Fall – MAT 2071 Proofs and Logic – Reitz

Theme by Anders Noren — Up ↑

Our goal is to make the OpenLab accessible for all users.

top

Our goal is to make the OpenLab accessible for all users.

## Leave a Reply