Logical Prior Probability - Institute for Creative Technologies
... The purpose of this paper is to present a prior over theories in first-order logic, similar in nature to the priors of algorithmic probability. There are several possible motivations for such a prior. First, it is hoped that the study of priors over logics will be useful to the study of realistic re ...
... The purpose of this paper is to present a prior over theories in first-order logic, similar in nature to the priors of algorithmic probability. There are several possible motivations for such a prior. First, it is hoped that the study of priors over logics will be useful to the study of realistic re ...
Exercise
... 2 is irrational • Suppose 2 is rational. Then 2 = p/q, such that p, q have no common factors. Squaring and transposing, p2 = 2q2 (even number) So, p is even (previous slide) Or p = 2x for some integer x So 4x2 = 2q2 or q2 = 2x2 So, q is even (previous slide) So, p,q are both even – they have a co ...
... 2 is irrational • Suppose 2 is rational. Then 2 = p/q, such that p, q have no common factors. Squaring and transposing, p2 = 2q2 (even number) So, p is even (previous slide) Or p = 2x for some integer x So 4x2 = 2q2 or q2 = 2x2 So, q is even (previous slide) So, p,q are both even – they have a co ...
Use Square Root
... In the first fomula, the irrational number Pi is used (as approximated by a calculator) and the resulting answer will be an irrational number. In the second formula, an approximation has already occurred but the calculation is commonly irrational as well. Both cases require the standard practice of ...
... In the first fomula, the irrational number Pi is used (as approximated by a calculator) and the resulting answer will be an irrational number. In the second formula, an approximation has already occurred but the calculation is commonly irrational as well. Both cases require the standard practice of ...
Latin squares and magic squares.
... The main diagonal of a n × n grid is simply the set of cells connecting the top-left to the bottomright cells: i.e. (1, 1), (2, 2), . . . (n, n). Similarly, the main antidiagonal is just the set of cells connecting the bottom-left to the top-right: i.e. (n, 1), (n − 1, 2), . . . (1, n). ...
... The main diagonal of a n × n grid is simply the set of cells connecting the top-left to the bottomright cells: i.e. (1, 1), (2, 2), . . . (n, n). Similarly, the main antidiagonal is just the set of cells connecting the bottom-left to the top-right: i.e. (n, 1), (n − 1, 2), . . . (1, n). ...
Section.1.1
... contradiction for any statement S. A truth table will show us that “if A then B,” is equivalent to “A and not B implies false.” So to prove “if A then B,” it suffices to assume A and also to assume not B, and then argue toward a false statement. This technique is called proof by contradiction or red ...
... contradiction for any statement S. A truth table will show us that “if A then B,” is equivalent to “A and not B implies false.” So to prove “if A then B,” it suffices to assume A and also to assume not B, and then argue toward a false statement. This technique is called proof by contradiction or red ...
Proof by Contradiction
... contradiction, because I assumed he was telling the truth. Hence, I’ve proved by contradiction that Calvin must be a liar. Hence, “Exactly one of us is lying” is false. This gives two possibilities: Either both are telling the truth, or both are lying. Suppose both are telling the truth. This contra ...
... contradiction, because I assumed he was telling the truth. Hence, I’ve proved by contradiction that Calvin must be a liar. Hence, “Exactly one of us is lying” is false. This gives two possibilities: Either both are telling the truth, or both are lying. Suppose both are telling the truth. This contra ...
