Predicate Logic
... • The domain of discourse U is all human beings. • “All human beings are mortal.” translates to x (H(x) M(x)) “Sachin is a human being.” translates to H(Sachin) • Therefore, for H(Sachin) M(Sachin) to be true it must be the case that M(Sachin). Later we will show this formally. Thursday, Januar ...
... • The domain of discourse U is all human beings. • “All human beings are mortal.” translates to x (H(x) M(x)) “Sachin is a human being.” translates to H(Sachin) • Therefore, for H(Sachin) M(Sachin) to be true it must be the case that M(Sachin). Later we will show this formally. Thursday, Januar ...
Math 201-103-RE Practice Assignment 5 Applications of the
... (76) The demand function for a product is given by p = 300 − x where p is the price per unit when x units are demanded. (a) Determine the intervals of elasticity of demand (b) If the price of the product at $15 increases by 1%, what is the approximate percentage in demand? (c) Will the total revenue ...
... (76) The demand function for a product is given by p = 300 − x where p is the price per unit when x units are demanded. (a) Determine the intervals of elasticity of demand (b) If the price of the product at $15 increases by 1%, what is the approximate percentage in demand? (c) Will the total revenue ...
Continuos Random Variables and Moment Generating Functions 1
... to each other: 1/λ = x/(α − 1). For further specification, suppose x = 1 so that α = λ + 1. In short, we compare Expo (λ) with Par (λ + 1, 1). In our comparison, we want to find an interval where the tail of Par (λ + 1, 1) is larger than the tail of Expo (λ): e−λx = P( Expo (λ) ≥ x ) ≤ P( Par (λ + 1 ...
... to each other: 1/λ = x/(α − 1). For further specification, suppose x = 1 so that α = λ + 1. In short, we compare Expo (λ) with Par (λ + 1, 1). In our comparison, we want to find an interval where the tail of Par (λ + 1, 1) is larger than the tail of Expo (λ): e−λx = P( Expo (λ) ≥ x ) ≤ P( Par (λ + 1 ...
connections to higher type Recursion Theory, Proof-Theory
... This lecture will begin with classical computability and soon go further towards more general structures. Indeed, the point I want to raise here, following the original program of Church, is that lambda calculus is not just one of the many formalisms for computations, but should be looked at as the ...
... This lecture will begin with classical computability and soon go further towards more general structures. Indeed, the point I want to raise here, following the original program of Church, is that lambda calculus is not just one of the many formalisms for computations, but should be looked at as the ...
Closed Sets of Higher
... on RX with some equation like (f u g)(x) := f (x) + g(x). Using the lambda calculus, we would write something like u := λf X→R g X→R xX .f (x) + g(x). Conceptually, this has the advantage of clarifying precisely what the free variables f, g, x are doing in the above expression, while also isolating ...
... on RX with some equation like (f u g)(x) := f (x) + g(x). Using the lambda calculus, we would write something like u := λf X→R g X→R xX .f (x) + g(x). Conceptually, this has the advantage of clarifying precisely what the free variables f, g, x are doing in the above expression, while also isolating ...
Mathematics: the divine madness
... realization of the simplest conceivable mathematical ideas. . . ” “We can discover by means of purely mathematical constructions . . . the key to understanding natural phenomena. . . ” “Experience remains, of course, the sole criterion of the physical utility of a mathematical construction. But the ...
... realization of the simplest conceivable mathematical ideas. . . ” “We can discover by means of purely mathematical constructions . . . the key to understanding natural phenomena. . . ” “Experience remains, of course, the sole criterion of the physical utility of a mathematical construction. But the ...
Section 2.1: What is a Function?
... 1. Definitions: A function f is a rule that assigns to each element x in a set A exactly one element f(x), in a set B. The set A is the domain of the function. f(x) is the image of x under f. The range is the set of all possible values of f(x) as x varies through the domain. 2. Know how to evaluate ...
... 1. Definitions: A function f is a rule that assigns to each element x in a set A exactly one element f(x), in a set B. The set A is the domain of the function. f(x) is the image of x under f. The range is the set of all possible values of f(x) as x varies through the domain. 2. Know how to evaluate ...
