1. Test question here
... 11. The Fibonacci sequence is defined such that the first two numbers in the sequence are both 1 and each successive number is the sum of the two previous numbers in the sequence. The first 5 numbers in the sequence are 1, 1, 2, 3, and 5. What is the greatest common divisor of the 23rd and 24th numb ...
... 11. The Fibonacci sequence is defined such that the first two numbers in the sequence are both 1 and each successive number is the sum of the two previous numbers in the sequence. The first 5 numbers in the sequence are 1, 1, 2, 3, and 5. What is the greatest common divisor of the 23rd and 24th numb ...
Formal logic
... Assume that we have a finite set Γ of assumptions. We then have two methods at our disposal to decide whether a given formula follows from Γ: either we build a syntactic proof, or show that all models of the assumptions also satisfy the formula. In particular, since we are working with a finite set ...
... Assume that we have a finite set Γ of assumptions. We then have two methods at our disposal to decide whether a given formula follows from Γ: either we build a syntactic proof, or show that all models of the assumptions also satisfy the formula. In particular, since we are working with a finite set ...
1 The Natural Numbers
... As our first application of RT, let’s show that the informal recursive definition of addition given above actually makes sense. To get started, suppose m ∈ ω. We’ll use RT to show there is a function Am such that Am (0) = m and Am (suc(n)) = suc(Am (n)). The trick, as always when applying RT, is to ...
... As our first application of RT, let’s show that the informal recursive definition of addition given above actually makes sense. To get started, suppose m ∈ ω. We’ll use RT to show there is a function Am such that Am (0) = m and Am (suc(n)) = suc(Am (n)). The trick, as always when applying RT, is to ...
Number Theory
... 1. What is the smallest 4-digit number that is divisible by 2, 3, 4, 5, 6, 8, 9, and 10? Reasoning: The number must end in zero. Lets assume that to be the smallest it should start with a 1. Since the digits must add up to 9, the last three digits must add up to 8. 1,080 is the smallest four-digit i ...
... 1. What is the smallest 4-digit number that is divisible by 2, 3, 4, 5, 6, 8, 9, and 10? Reasoning: The number must end in zero. Lets assume that to be the smallest it should start with a 1. Since the digits must add up to 9, the last three digits must add up to 8. 1,080 is the smallest four-digit i ...
Section 2.1: Shift Ciphers and Modular Arithmetic
... Modular Arithmetic • As the last two examples illustrate, one must know the key k used in a shift cipher when deciphering a message. This leads to an important question. How can we decipher a message in a shift cipher if we do not know the key k? Cryptanalysis is the process of trying to break a cip ...
... Modular Arithmetic • As the last two examples illustrate, one must know the key k used in a shift cipher when deciphering a message. This leads to an important question. How can we decipher a message in a shift cipher if we do not know the key k? Cryptanalysis is the process of trying to break a cip ...
Structural Multi-type Sequent Calculus for Inquisitive Logic
... collections of teams, and are denoted by the variables X, Y and Z, possibly suband super-scripted. The operation ⇒ is defined as follows: for any Y and Z, Y ⇒ Z := {S | for all S ′ , if S ′ ⊆ S and S ′ ∈ Y, then S ′ ∈ Z}. Three natural maps can be defined between the perfect Boolean algebra B and th ...
... collections of teams, and are denoted by the variables X, Y and Z, possibly suband super-scripted. The operation ⇒ is defined as follows: for any Y and Z, Y ⇒ Z := {S | for all S ′ , if S ′ ⊆ S and S ′ ∈ Y, then S ′ ∈ Z}. Three natural maps can be defined between the perfect Boolean algebra B and th ...
![CS 512, Spring 2017, Handout 05 [1ex] Semantics of Classical](http://s1.studyres.com/store/data/001902216_1-d85c63c8a0994ab9df7b1ab59a6b4141-300x300.png)
CS 512, Spring 2017, Handout 05 [1ex] Semantics of Classical
... Let Γ a (possibly infinite) set of propositional WFF’s. If, for every model/interpretation/valuation (i.e., assignment of truth values to prop atoms), it holds that: I ...
... Let Γ a (possibly infinite) set of propositional WFF’s. If, for every model/interpretation/valuation (i.e., assignment of truth values to prop atoms), it holds that: I ...
MARTIN`S CONJECTURE, ARITHMETIC EQUIVALENCE, AND
... invariant function that is increasing a.e., then there exists an α < ω1 so that f (x) ≡T xα a.e. The proof of this theorem uses a generalization of the Posner-Robinson theorem for iterates of the Turing jump up through ω1 . To generalize this theorem beyond the Borel functions, it would be enough to ...
... invariant function that is increasing a.e., then there exists an α < ω1 so that f (x) ≡T xα a.e. The proof of this theorem uses a generalization of the Posner-Robinson theorem for iterates of the Turing jump up through ω1 . To generalize this theorem beyond the Borel functions, it would be enough to ...
infinite perimeter of the Koch snowflake and its finite - Dimes
... calculus and related to limits with an argument tending to ∞ or zero. The numeral system from [27,29,31,43] has allowed the author to propose a corresponding computational methodology and to introduce the Infinity Computer (see the patent [34]) being a supercomputer working numerically with a variet ...
... calculus and related to limits with an argument tending to ∞ or zero. The numeral system from [27,29,31,43] has allowed the author to propose a corresponding computational methodology and to introduce the Infinity Computer (see the patent [34]) being a supercomputer working numerically with a variet ...
