printable
... • one-to-one if no two elements in A match to the same element in B • onto Each element in B is mapped to by at least one element in A • a bijection if it is both one-to-one and onto The inverse of a binary relation R ⊂ A × B is denoted R−1 , and defined to be {(b, a) : (a, b) ∈ R} • A function only ...
... • one-to-one if no two elements in A match to the same element in B • onto Each element in B is mapped to by at least one element in A • a bijection if it is both one-to-one and onto The inverse of a binary relation R ⊂ A × B is denoted R−1 , and defined to be {(b, a) : (a, b) ∈ R} • A function only ...
CountableSets1
... many numbers. Much of calculus was about adding sequences of numbers. But sequences can have only countably many terms, so our theory of addition only allows us to add countable sets of numbers. The sum in the equation above involves an uncountable set of numbers. It looks easy because all the terms ...
... many numbers. Much of calculus was about adding sequences of numbers. But sequences can have only countably many terms, so our theory of addition only allows us to add countable sets of numbers. The sum in the equation above involves an uncountable set of numbers. It looks easy because all the terms ...
Identity and Philosophical Problems of Symbolic Logic
... There are philosophical issues concerning the status of sentence connectives in predicate logic. ...
... There are philosophical issues concerning the status of sentence connectives in predicate logic. ...
Prolog arithmetic
... Each operator has a precedence value associated with it. Precedence values are used to decide which operator is carried out first. In Prolog, multiplication and division have higher precedence values than addition and subtraction. ...
... Each operator has a precedence value associated with it. Precedence values are used to decide which operator is carried out first. In Prolog, multiplication and division have higher precedence values than addition and subtraction. ...
Chapter 1 Logic and Set Theory
... is not a tautology. That is, P → R certainly does not imply (P → Q) ∧ (Q → R). A logical implication that is reversible is called a logical equivalence. More precisely, P is equivalent to Q if the statement P ↔ Q is a tautology. We denote the sentence “P is equivalent to Q” by simply writing “P ⇔ Q. ...
... is not a tautology. That is, P → R certainly does not imply (P → Q) ∧ (Q → R). A logical implication that is reversible is called a logical equivalence. More precisely, P is equivalent to Q if the statement P ↔ Q is a tautology. We denote the sentence “P is equivalent to Q” by simply writing “P ⇔ Q. ...
Algebra 1 Lesson 5
... A Relation is a set of ordered pairs. The Domain of a relation is the set of first coordinates of the ordered pairs. ...
... A Relation is a set of ordered pairs. The Domain of a relation is the set of first coordinates of the ordered pairs. ...
Homework 3
... (a) The identity element for + (LCM) is 1 and that for · (GCF) is 30. (b) The complement of an element can be obtained by dividing 30 by that element. (c) This system is a Boolean algebra. ...
... (a) The identity element for + (LCM) is 1 and that for · (GCF) is 30. (b) The complement of an element can be obtained by dividing 30 by that element. (c) This system is a Boolean algebra. ...
From proof theory to theories theory
... From axioms to algorithms An important question about Deduction modulo is how strong the congruence can be. For instance, can we take a congruence such that A is congruent to ⊤ if A is a theorem of arithmetic, in which case each proof of each theorem is a proof of all theorems? This seems to be a ba ...
... From axioms to algorithms An important question about Deduction modulo is how strong the congruence can be. For instance, can we take a congruence such that A is congruent to ⊤ if A is a theorem of arithmetic, in which case each proof of each theorem is a proof of all theorems? This seems to be a ba ...
Lecture 34 Notes
... Next Mike shows that Musser’s attempted fix also fails. That was for the programming language Euclid. He comments that in our book, A Programming Logic, 1978, we use a total correctness logic to avoid these problems. The Nuprl type theory deals with partial correctness using partial types.We will ex ...
... Next Mike shows that Musser’s attempted fix also fails. That was for the programming language Euclid. He comments that in our book, A Programming Logic, 1978, we use a total correctness logic to avoid these problems. The Nuprl type theory deals with partial correctness using partial types.We will ex ...
