PPT-Infinite Sets

PHIL 2000 Tools for Philosophers 1 st Term 2016 Topics for Discussion What are sets Where are they How do they relate to their members Do they exist How are they different from Venn diagrams. Raymond Flood. Gresham Professor of Geometry. Georg Cantor . 1845 . – . 1918. Cantor’s infinities. Bronze . monument . to Cantor in . Halle-Neustadt. Georg Cantor . 1845 . – . 1918. Sets. One-to-one correspondence. Homework. HW8 due Tues 5/29 11am. HW5 grades are out. Monday is Memorial Day; no office hours, etc.. Go see a parade, or some fireworks, or something. TA Evaluations at the end of class. !. There’s a lot of stuff in today’s lecture. Dr. Cynthia Bailey Lee. Dr. . Shachar. Lovett. .  .                          . Peer Instruction in Discrete Mathematics by . Cynthia . Lee. is. licensed under a . Creative Commons Attribution-. Numbers . Integers . Rational. . Numbers. Real Numbers . ℝ. . . Insert . each of the following numbers in . the . correct place on the diagram. :. 5. . , . 6.. , 2. ,. -3, . , 0 and -. . .  . Anthony Bonato. Ryerson University. East Coast Combinatorics Conference. co-author. talk. post-doc. Into the infinite. R. Infinite random geometric graphs. 111. 110. 101. 011. 100. 010. 001. 000. Some properties. Sets. 2.2 Set Operations. 2.3 Functions. 2.4 Sequences and Summations. Sequences and Summations. Summation Notation. Cardinality. Some . Countably. Infinite Sets. Cantor . Diagonalization. P. 1. Definition: . 1. John D. Norton. Department of History and Philosophy of Science. University of Pittsburgh. Based on “Infinite Lottery Machines” in . The Material Theory. . of Induction.. Draft at http://. www.pitt.edu. Week . 11: Consequences. (Hilbert, 1922). Overview. In this session we look briefly at three results about infinity:. Cantor’s Theorem . tells us that classical set theory guarantees not only one infinity but an endless chain of them. It seems to be impossible to keep infinity “limited”.. and Matrices. Chapter 2. With Question/Answer Animations. Copyright © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill . The Language of Sets. Objective. Use three methods to represent sets.. Define and recognize the empty set.. Use the symbols and .. Apply set notation to sets of natural numbers.. Determine a set’s cardinal number.. All graphics are attributed to:. Calculus,10/E. by Howard Anton, Irl Bivens, and Stephen Davis. Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.”. Introduction. The purpose of this section is to discuss sums that contain infinitely many terms. Section. . 2.4. Cardinality. How can we compare the sizes of two sets?. If . S. = {. x.  . .   .  . : . x. 2. = 9}, then . S.  = {–3,.  . 3} and we say that . S. has two elements.. For example, to which populations do you belong? Do you categorize yourself as a college student?. What about your gender?. What about your academic major or your ethnic background?. Our minds cannot find order and meaning without creating collections. . John D. Norton. Department of History and. Philosophy of Science. University of Pittsburgh. SWC Scientific World Conceptions. University of Vienna. Summer School. July 2 to July 13, 2018 . What is it?.