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. Infinity. What is a set?. A . set. as any collection of well-defined objects, which we usually denote with . { } . .. 1. π. -12.652. 2. 3. ,. ,. ,. …, -2, -1, 0, 1, 2, …. Finite sets. We say a set is . 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-. 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: . 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”.. infinite random geometric . g. raphs. Anthony Bonato. Ryerson University. Random Geometric Graphs . and . Their Applications to Complex . Networks. BIRS. R. Infinite random geometric graphs. 111. 110. 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.. 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. . Anthony Bonato. Ryerson University. CRM-ISM Colloquium. Université. Laval. Complex networks in the era of . Big Data. web graph, social networks, biological networks, internet networks. , …. Infinite random geometric graphs - Anthony Bonato. David J. Stucki. Alerts. FYS announcement.... Pythagorean Triples & Euclid's Primes due today. Archimedes . calculations.... This worksheet will be due next Wednesday!. 12 of 40 . FYE . reports (7 days left). a’ . be an element of A , then we write . and read it as ‘ a . belongs . to . A’ . or ‘ a is an element of . A’. If a is not an element of A then . SET BUILDER FORM.