PPT-Turing and Ordinal Logic

14 th September 2012 Turing and Ordinal Logic Or To Infinity and Beyond James Harland School of Computer Science amp IT RMIT University jamesharlandrmiteduau Turing at Princeton. Please do not alter or modify contents All rights reserved For more information call 8003384065 or visit wwwloveandlogiccom Love and Logic Institute Inc is located at 2207 Jackson Street Golden CO 80401 57513 1998 Jim Fay 57375e Delayed or Anticipat Vinay Singh. MARCH 20, 2012. MAT 7670. Introduction to Ordinal Numbers. Ordinal Numbers. Is an . extension (domain ≥) . of Natural Numbers (ℕ) different from Integers (ℤ) and Cardinal numbers (Set sizing). BY JOHN NAGUIB. What is Logic?. The science or study of how to evaluate arguments and reasoning. . “Logic is new and necessary reasoning” -Aristotle. Studied within. Philosophy. Mathematics. Computer Science. By: Brittany Newman . Henry the Fourth . Henry The Fourth . Annotation:. Murphy . , S. (1998). . Henry the . fourth: . Ordinals (. mathstart. 1 series). . New . York. , NY: . HarperCollins Publishers .. the Halting Problem. This work is licensed under the Creative Commons Attribution-. NonCommercial. -. ShareAlike. 3.0 . Unported. License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041, USA.. Computability and Logic. Central Question. Given any statement about mathematics, is it true or is it false?. Example: . Goldbach. Conjecture: Every even number greater than 2 is the sum of two prime numbers.. Machines. Recursive and Recursively Enumerable Languages. Turing Machine. 1. Turing-Machine Theory. The purpose of the theory of Turing machines is to prove that certain specific languages have no algorithm.. Handy Ordinal Numbers. Hello! I am Miss Digitally Angry . Clock-Face, and I am here to teach you ordinal numbers. So, . pay attention.. Ordinal numbers show you which order things are in. (Just in case you didn’t know.). Tom Wildenhain. Introduction. As many users are well-aware, Microsoft PowerPoint ® offers unparalleled presentation editing tools, enabling the creation of professional, animation-laden slides with minimal effort (Source: Microsoft).. . 22-25 June 2012. Overview and Summary. Michael Brand. Manchester town hall. Venue. The 12 “Manchester Murals”. Color-lit. 16-foot. pipe organ. Stars & planets depicted in . mozaic. City & country crests. In-Class Activity…. Roadmap. Worksheets will not be returned . In-class activities . reinforce. what was covered in. Assigned reading. Assigned videos. Lecture. Worksheets . do NOT include new material . The Turing Test Minds & Machines Alan Turing British mathematician known for: Turing Machines (1936) Breaking German Enigma (WWII) Turing Test (1950) ? “I propose to consider the question, 'Can machines think?' This should begin with definitions of the meaning of the terms 'machine 'and 'think'. … [But] Instead of attempting such a definition I shall replace the question by another... The new form of the problem can be described in terms of a game which we call the 'imitation game'.“ In this topic, we will:. Ask what is computable. Describe a Turing machine. Define Turing completeness. Computability. How do we define what is and what is not computable?. Is it possible to write a C++ function which cannot be written using Pascal, Java, or C#, or vice versa?. What is Logic?. The science or study of how to evaluate arguments and reasoning. . “Logic is new and necessary reasoning” -Aristotle. Studied within. Philosophy. Mathematics. Computer Science. When did it start??.