chap1sec7 - University of Virginia, Department of Computer
... logical equivalences. This is table 1 on page 89 of the text. Take a look at this table and compare it to our table for logical equivalences. You will find them to be strikingly similar. This is not a coincidence. Every set operation that we introduced could be expressed in set builder notation usin ...
... logical equivalences. This is table 1 on page 89 of the text. Take a look at this table and compare it to our table for logical equivalences. You will find them to be strikingly similar. This is not a coincidence. Every set operation that we introduced could be expressed in set builder notation usin ...
Complex Numbers - Henri Picciotto
... Natural numbers, integers, rational numbers, and real numbers can all be found on a one-dimensional number line. However, to solve equation (g), you need to get off the number line! The solution is a complex number, and it is written 3i. The number i is a number one unit away from 0, but off the num ...
... Natural numbers, integers, rational numbers, and real numbers can all be found on a one-dimensional number line. However, to solve equation (g), you need to get off the number line! The solution is a complex number, and it is written 3i. The number i is a number one unit away from 0, but off the num ...
Slides 08
... What do we mean by “behave the way that random numbers would”? If the numbers run 0.0 to 1.0, then 1/n of them should fall into any interval of length 1/n Similarly for 2 dimensions, 3 dimensions, etc. Shouldn’t be able to predict the next from the previous, or the next from the two previous, or the ...
... What do we mean by “behave the way that random numbers would”? If the numbers run 0.0 to 1.0, then 1/n of them should fall into any interval of length 1/n Similarly for 2 dimensions, 3 dimensions, etc. Shouldn’t be able to predict the next from the previous, or the next from the two previous, or the ...
Weak MSO+U over infinite trees
... I Theorem 1. Satisfiability is decidable for WMSO+U over infinite trees. We prove the theorem in three steps. 1. In Section 1, we define a new automaton model for infinite trees, called a nested limsup automaton, which has the same expressive power as WMSO+U, and show effective translations from the ...
... I Theorem 1. Satisfiability is decidable for WMSO+U over infinite trees. We prove the theorem in three steps. 1. In Section 1, we define a new automaton model for infinite trees, called a nested limsup automaton, which has the same expressive power as WMSO+U, and show effective translations from the ...
How fast does a continued fraction converge?
... of continued fractions, cfs. We study complex and periodic cfs. Of special interest is the cf in which the period is 1: Let b be any positive number and u(b) be the positive root of the quadratic equation x2 bx 1 = 0. We show how to compute the rate at which the cf with all an = b converges to u(b). ...
... of continued fractions, cfs. We study complex and periodic cfs. Of special interest is the cf in which the period is 1: Let b be any positive number and u(b) be the positive root of the quadratic equation x2 bx 1 = 0. We show how to compute the rate at which the cf with all an = b converges to u(b). ...
Random Number Generation
... Cycle length (P) depends on the choice of parameters (always less than m) For m = 2b, c 0 and relatively prime to m and a = 1+4k, the longest possible period P = m. For m = 2b, c = 0, X0 (seed) odd, and a = 3+8k or a = 5+8k, the longest possible period P = m/4 For m a prime number, etc.. P = m-1 ...
... Cycle length (P) depends on the choice of parameters (always less than m) For m = 2b, c 0 and relatively prime to m and a = 1+4k, the longest possible period P = m. For m = 2b, c = 0, X0 (seed) odd, and a = 3+8k or a = 5+8k, the longest possible period P = m/4 For m a prime number, etc.. P = m-1 ...
INTRODUCING INTEGERS - Mrs. Murphy's 6th Grade Class
... Let’s say your parents bought a car but had to get a loan from the bank for $5,000. When counting all their money they add in -$5.000 to show they still owe the bank. ...
... Let’s say your parents bought a car but had to get a loan from the bank for $5,000. When counting all their money they add in -$5.000 to show they still owe the bank. ...
Infinity
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.In mathematics, ""infinity"" is often treated as if it were a number (i.e., it counts or measures things: ""an infinite number of terms"") but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number; see 1/∞.Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.