Tag: Open Lab #6
Logic on Math StackExchange
- Why does $\forall n \in \mathbb{N} \vdash P(n)$ not imply $\forall n \in \mathbb{N}P(n)$? June 22, 2024I am trying to understand why $\forall n \in \mathbb{N} \vdash P(n)$ doesn't imply $\forall n \in \mathbb{N}P(n)$ by studying the concepts in this answer, and had 2 questions about the difference between $\forall n \in \mathbb{N} \vdash P(n)$ and $\forall n \in \mathbb{N}P(n)$: Why does $\forall n \in \mathbb{N} \vdash P(n)$ only make sense […]Princess Mia
- Example of a proof system that is complete but not sound June 22, 2024i'm trying to give an example of a proof system that is complete but not sound . i tried this : Axioms : all WFF rule of infernce : MP . then i claimed : given set $A$ and $a$ in WFF , if $ A |= a $ then $A |- a $ because […]sami younis
- Why is $\{A \land \neg A\} \vdash \neg\neg B$ in this deduction tree? June 22, 2024I'm reading through an introduction to logic textbook and cannot follow an example on natural deduction rules. I couldn't find a way to nicely typeset the deduction tree in MathJax, so I'll instead name each deduction with a roman numeral and build the tree by referencing those names; please do advise me on a better […]Emma
- Why doesn't this diagonal argument work? June 22, 2024I have a question about the standard rules for computing p.r. terms (see below). It seems pretty clear that these rules could be used to define a p.r. operation that evaluates any p.r. term of the form $f_n(n)$. But we know that such an operation does not exist, due to diagonalization arguments. What am I […]nontology
- How would it be possible to encoding a row and a column with a single number? But the row or column or both are negative June 21, 2024I know that you can represent a row and column in a single number by multiplying the row by a number and adding the column, for example 5 * 8 + 3 = 43 And 43 is: row: 8/43 = 5.375 = 5 column: 43 mod 8 = 3 And that number 43 would have […]Sleep
- seating arrangement for 54 people at 9 tables switching tables and groups 4 times [closed] June 21, 2024I have 54 people and 9 tables. I want the people to be spread out over the tables. Then they switch tables such that they sit with different people. I want people to switch 4 times, each time sitting with different people. Could you provide me with the seating arrangement for each of the 4 […]Kai Polak
- Why do we need a metatheory if we can include self-referencing language in the object theory? June 21, 2024I am wondering why we need to have a metatheory in order to talk about a theory- why can't we just add self-referencing terms to the language of the formal system on which the theory itself is based, such that all of the statements we make in a metatheory can be made in its object […]Princess Mia
- The connection between logic and algebraic manipulations June 21, 2024I've been studying logic as part of my Discrete Mathematics course and I understood most of the material so far: statements, predicates, connectives, arguments, etc. The book was very thorough and the material clear, however, now that it is moving to proofs of actual mathematical theorems, I feel it became much sloppier in explaining what's […]Daniel
- Finding the coordinate of four points of imaginary intersecting lines which passes through end points of two intersecting lines June 21, 2024image I want to find the coordinates of the points A,B,C,D where two imaginary lines intersect each other, where this imaginary lines passes through the end points of the two lines L1 and L2, the imaginary lines AB and DC are parallel to line L2 and the imaginary lines AD and BC are parallel to […]Basavaraj Kittali
- What is the formal system when we are using many different sets of axioms? June 21, 2024I am just starting to learn about formal systems, and have learnt that the many axiom systems in Mathematics, such as those of plane geometry, Peano's axioms, vector axioms, etc. can each be used to form different formal systems. However, in informal mathematics, we often couple multiple branches together, e.g. like when we use the […]Princess Mia
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