Lecture Notes
... Note that the proof actually shows that if φ is satisfiable iff there exists a model for φ with 2|φ| worlds. This implies that there is an algorithm that decides if φ is satisfiable: Construct all structures of size 2 ...
... Note that the proof actually shows that if φ is satisfiable iff there exists a model for φ with 2|φ| worlds. This implies that there is an algorithm that decides if φ is satisfiable: Construct all structures of size 2 ...
Full text
... Theorem 1: (Brison) Let p ≥ 5 be a prime number. A Φ2 -sequence (an )n is a complete Fibonacci sequence if and only if an = bn for all n, where b is a Fibonacci primitive root. The new results of this paper concern the case κ = 3. Because of the specific recurrence satisfied by Φ3 -sequences (an+3 = ...
... Theorem 1: (Brison) Let p ≥ 5 be a prime number. A Φ2 -sequence (an )n is a complete Fibonacci sequence if and only if an = bn for all n, where b is a Fibonacci primitive root. The new results of this paper concern the case κ = 3. Because of the specific recurrence satisfied by Φ3 -sequences (an+3 = ...
On Rosser sentences and proof predicates
... predicate P r as the necessity operator in some suitable modal logic, and much work on modal fixed points was done in the seventies by C. Bernardi, D. de Jongh and G. Sambin. It was proven independently by the three that modal fixed points are unique, and de Jongh and Sambin also presented proofs ...
... predicate P r as the necessity operator in some suitable modal logic, and much work on modal fixed points was done in the seventies by C. Bernardi, D. de Jongh and G. Sambin. It was proven independently by the three that modal fixed points are unique, and de Jongh and Sambin also presented proofs ...
equivalent forms
... Critical to understanding mathematics is the concept of equivalent forms. Equivalent forms are used throughout this course. Throughout mathematics one encounters equivalent forms of numbers, equivalent forms of expressions, equivalent forms of equations, equivalent forms of functions, equivalent for ...
... Critical to understanding mathematics is the concept of equivalent forms. Equivalent forms are used throughout this course. Throughout mathematics one encounters equivalent forms of numbers, equivalent forms of expressions, equivalent forms of equations, equivalent forms of functions, equivalent for ...
Holt McDougal Algebra 1 Solving Inequalities by Multiplying or
... Solve each inequality and graph the solutions. a. 10 ≥ –x –1(10) ≤ –1(–x) ...
... Solve each inequality and graph the solutions. a. 10 ≥ –x –1(10) ≤ –1(–x) ...
Section 1.2-1.3
... In a proof of a statement (8n b) P (n) by mathematical induction, b is referred to as the base value. The proof of P (b) is called the base step and the proof of (8n b) [P (n) ! P (n + 1)] is called the inductive step. In the latter proof diagram of proof strategy 1.3.1, the assumption P (n) is call ...
... In a proof of a statement (8n b) P (n) by mathematical induction, b is referred to as the base value. The proof of P (b) is called the base step and the proof of (8n b) [P (n) ! P (n + 1)] is called the inductive step. In the latter proof diagram of proof strategy 1.3.1, the assumption P (n) is call ...
Discrete Mathematics
... Now consider 4 photos. There would be 5 · 4! = 5! possible arrangements. Extrapolating to 30 photos, we would get 31 · 30! = 31! possible arrangements. b) In how many ways can I post these photos to the web pages if the order in which the photos appear on those pages does not matter? In the case whe ...
... Now consider 4 photos. There would be 5 · 4! = 5! possible arrangements. Extrapolating to 30 photos, we would get 31 · 30! = 31! possible arrangements. b) In how many ways can I post these photos to the web pages if the order in which the photos appear on those pages does not matter? In the case whe ...
CHAPTER 8 Hilbert Proof Systems, Formal Proofs, Deduction
... Theorem 3.1 (Deduction Theorem for H2 ) For any subset Γ of the set of formulas F of H2 and for any formulas A, B ∈ F , Γ, A `H2 B if and only if Γ `H2 (A ⇒ B). In particular, A `H2 B if and only if `H2 (A ⇒ B). Obviously, the axioms A1, A2, A3 are tautologies, and the Modus Ponens rule leads from t ...
... Theorem 3.1 (Deduction Theorem for H2 ) For any subset Γ of the set of formulas F of H2 and for any formulas A, B ∈ F , Γ, A `H2 B if and only if Γ `H2 (A ⇒ B). In particular, A `H2 B if and only if `H2 (A ⇒ B). Obviously, the axioms A1, A2, A3 are tautologies, and the Modus Ponens rule leads from t ...
aLgebraic expression
... A collection of constants and variables connected by one or more of the operations of addition, subtraction, multiplication and division is called an algebraic expression. For example, 4x + 5, 9y – 13 are algebraic expressions. The expression 4x + 5 is formed, first multiplying the variable x by the ...
... A collection of constants and variables connected by one or more of the operations of addition, subtraction, multiplication and division is called an algebraic expression. For example, 4x + 5, 9y – 13 are algebraic expressions. The expression 4x + 5 is formed, first multiplying the variable x by the ...
