The Calculi of Lambda-Conversion by Alonzo Church Annotated
... We now introduce the fundamental operations on well-formed formulas in λ-Calculus: conversion. Although there are many forms of conversion, these are the three we begin with: I Given a formula, we can replace any part M with M [x := y] as long as x is not a free variable of M and y does not occur in ...
... We now introduce the fundamental operations on well-formed formulas in λ-Calculus: conversion. Although there are many forms of conversion, these are the three we begin with: I Given a formula, we can replace any part M with M [x := y] as long as x is not a free variable of M and y does not occur in ...
Lecture 10: A Digression on Absoluteness
... The somewhat surprising answer is: no! “Just because A thinks it is well-founded. . . ” In fact, we can actually show the following theorem. Theorem 8.4. If A is an infinite structure with arbitrarily long finite chains, then there exists a non-well-founded structure B such that B ≡ A. To prove this ...
... The somewhat surprising answer is: no! “Just because A thinks it is well-founded. . . ” In fact, we can actually show the following theorem. Theorem 8.4. If A is an infinite structure with arbitrarily long finite chains, then there exists a non-well-founded structure B such that B ≡ A. To prove this ...
Document
... Summary of How to Find the Domain of a Function • Look for any fractions or square roots that could cause one of the two "illegals" to happen. If there aren't any, then the domain is All real numbers x. • If there are fractions, figure out what values would make the bottom equal zero and those are ...
... Summary of How to Find the Domain of a Function • Look for any fractions or square roots that could cause one of the two "illegals" to happen. If there aren't any, then the domain is All real numbers x. • If there are fractions, figure out what values would make the bottom equal zero and those are ...
Lesson 2-1
... Find the domain and range. Since x can be any real number, there is an infinite number of ordered pairs that can be graphed. All of them lie on the line shown. Notice that every real number is the x-coordinate of some point on the line. Also, every real number is the y-coordinate of some point on th ...
... Find the domain and range. Since x can be any real number, there is an infinite number of ordered pairs that can be graphed. All of them lie on the line shown. Notice that every real number is the x-coordinate of some point on the line. Also, every real number is the y-coordinate of some point on th ...
Solutions to RMO-2014 problems
... squares, with one number in each square, such that the product of the numbers in each 2×2 sub-grids AM RG, GRN D, M BHR and RHCN is divisible by 16? Solution: NO! If the product in each 2 × 2 sub-square is divisible by 16, then the product of all the numbers is divisible by 16 × 16 × 16 × 16 = 216 . ...
... squares, with one number in each square, such that the product of the numbers in each 2×2 sub-grids AM RG, GRN D, M BHR and RHCN is divisible by 16? Solution: NO! If the product in each 2 × 2 sub-square is divisible by 16, then the product of all the numbers is divisible by 16 × 16 × 16 × 16 = 216 . ...
Section 1
... 1. State the domain of the function. 2. Compute f and f . 3. Find the critical numbers, which are values of x where either f ( x) 0 or f (x) is undefined. Find the y coordinates of these points by substituting these x values back into the original function f (x) . These points represent the ...
... 1. State the domain of the function. 2. Compute f and f . 3. Find the critical numbers, which are values of x where either f ( x) 0 or f (x) is undefined. Find the y coordinates of these points by substituting these x values back into the original function f (x) . These points represent the ...
Section 10.1
... Because each nonnegative real number x has exactly one principal square root, x , there is a square root function defined by f x The domain of this function is 0, ...
... Because each nonnegative real number x has exactly one principal square root, x , there is a square root function defined by f x The domain of this function is 0, ...
ON FINITE SUMS OF RECIPROCALS OF DISTINCT
... where ζ(3) = Σ*U &~3 = 1.2020569REMARKS. In theory it should be possible to calculate directly from the relevant theorems (cf., [2], [3]) an explicit bound for the number of terms of Hn needed to represent p\q as an element of P(Hn). However, since the theorems were not designed to minimize such a b ...
... where ζ(3) = Σ*U &~3 = 1.2020569REMARKS. In theory it should be possible to calculate directly from the relevant theorems (cf., [2], [3]) an explicit bound for the number of terms of Hn needed to represent p\q as an element of P(Hn). However, since the theorems were not designed to minimize such a b ...