Conjecture:

“What restrictions can be placed on the maximum and minimum number of visits per vertices?” Continue reading

Skip to the content

Conjecture:

“What restrictions can be placed on the maximum and minimum number of visits per vertices?” Continue reading

- Multiway graph derived from a simple rule: why this first step? June 10, 2023In https://writings.stephenwolfram.com/2022/03/the-physicalization-of-metamathematics-and-its-implications-for-the-foundations-of-mathematics/#mathematics-and-physics-have-the-same-foundations some examples are given of multiway graphs when applying a given rule. One of these examples is I don't understand the first step of the derivation. From $a \circ x_$ applying the rule $x_ \longleftrightarrow y_$ left to right I see very well we get $ a \circ y_ $, but how do […]kiriloff
- Introductory text on logic for those interested in the intersection of logic, algebra, and topology? June 9, 2023I'm a current MA student doing research in formal semantics, which is an application of, among other things, logic and model theory to the study of the semantics of natural languages. I'd like to build up a stronger foundation in formal logic before tackling other topics / projects. I love the interplay between logic, algebra, […]m. lekk
- Definability of eventually periodic June 9, 2023Let $\Bbb{N}$ the set of natural numbers including 0. A set $X\subset \Bbb{N}$ is called eventually periodic if there is a $p\geq 1$ and an $n_0 \in \Bbb{N}$ such that for all $n \geq n_0$ we have $$n \in X \leftrightarrow n + p \in X $$ Let $\mathcal{L}=\{0,+,S\}$ be a language where $0$ is […]Superdivinidad
- Suppose $R$ is a relation on $A$. Let $S$ be the transitive closure of $R$. Then $Dom(S)\subset Dom(R)$ June 8, 2023$Proof$. Suppose $x\in Dom(S)$ and $x\notin Dom(R)$. Then there is some $y\in A$ such that $xSy$. Since $S$ is the transitive closure of $R$, there exist some set of pairs in $R$ such that $x$ and $y$ can be connected. But $x\notin Dom(R)$, so this connection cannot be made. Therefore it must be that $x\in […]lightyourassonfire
- Is Tarski's exponential function problem arithmetically decidable? June 8, 2023https://en.wikipedia.org/wiki/Tarski%27s_exponential_function_problem shows a very interesting problem, as for me begging for an undecidability proof (as the Tarski-Seidenberg theorem itself is already very strong, and this would strengthen it a lot more) But is it decidable with an oracle for arithmetical truth? (Given an arithmetical sentence, this oracle will return whether it is true or false) […]Alexey Slizkov
- Is there some variant of sequent calculus that allows for non-trivial axioms? June 8, 2023Apologies if the question doesn't make sense: it's one of those cases where my confusion is so diffuse that I'm not even sure how to ask the question. In short, I would like to know if it's possible, within some variant of sequent calculus, to prove the sequent $$ \varGamma \,\vdash\, V $$ starting from […]pglpm
- When does a proof have too little details? (prove that the reflexive closure of a strict partial order is a partial order) June 8, 2023Suppose $R$ is a strict partial order on $A$. Let $S$ be the reflexive closure of $R$. Then $S$ is a partial order on $A$. $Proof.$ $R$ is transitive and antisymmetric, and $i_A$ is reflexive. So since $S$ is just $R\cup i_A$, $S$ is a partial order on $A$. $\square$ Does this proof have too […]lightyourassonfire
- Henkin's Model Existence Theorem and Forcing June 8, 2023Henkin's Model Existence Theorem says that, if $T$ is a consistent theory, then there exists some set $S$ such that $S \models T$. Suppose we are trying to prove the theorem $\text{Con}(ZFC) \rightarrow \text{Con}(ZFC + \neg CH)$. Are the following steps a correct way to start? Assume $\text{Con}(ZFC)$. Use Henkin's Model Existence Theorem to get […]Gavin Dooley
- Doing a commentary of a proof (if a poset has a unique minimal and that minimal is not the smallest, then the poset is infinite) June 8, 2023The initial proposition was: "If a subset of a partially ordered set has exactly one minimal element, must that element be a smallest element?" And here is a proof: https://math.stackexchange.com/a/2280977/1184854 But this doesnt directly proof the proposition right? They prove a little bit different proposition. Here is my commentary of the proof: The proposition is […]lightyourassonfire
- Expressability in notation of set theory June 8, 2023The following from Terence Tao's blog dated 2007-08-27: It seems that one cannot express For every x and x’, there exists a y depending only on x and a y’ depending only on x’ such that Q(x,x’,y,y’) is true (*) in first order logic! https://terrytao.wordpress.com/2007/08/27/printer-friendly-css-and-nonfirstorderizability/#more-172 Does the following adequately formalize this statement using the notation […]Dan Christensen

"Math Improve"
.999
1
assignment
assignments
calculus
exam #3
exam 3 grades
final papers
grading criteria
grading policy
graph theory
group
group paper
group project
homework
mathography
metacognition
openlab
OpenLab #4: Bridges and Walking Tours
Open Lab #6
OpenLab7
OpenLab 8
OpenLab8
Open Lab 8
Openlab8 Vi Hart
openlab assignment
perfect circle
points
presentation
project
resource
rubric
semester project
spring classes
Stars
vi hart
ViHart
visual math
Wau
webwork
week 8
week 14
welcome
written work

© 2023 2017 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.

## Recent Comments