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1. www.math.toronto.edu › weiss › set_theoryAN INTRODUCTION TO SET THEORY - University of Toronto ...

   www.math.toronto.edu › weiss › set_theory

   A book-in-progress on set theory, covering the basics, the axioms, the paradoxes, and the open problems. Learn the language, logic, and mathematics of sets with examples and exercises.

   • File Size: 405KB

   • Page Count: 119

2. www.math.uh.edu › ~dlabate › settheory_AshlockBasic Set Theory - UH

   www.math.uh.edu › ~dlabate › settheory_Ashlock

   Basic Set Theory. A set is a Many that allows itself to be thought of as a One. - Georg Cantor This chapter introduces set theory, mathematical in- duction, and formalizes the notion of mathematical functions. The material is mostly elementary. For those of you new to abstract mathematics elementary does not mean simple (though much of the ...

   • File Size: 246KB

   • Page Count: 20

3. People also ask

   What are the basic concepts of set theory?

   • 1. Basic Concepts of Set Theory. 1.1. Sets and elements Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions.

   Basic Concepts of Set Theory, Functions and Relations - UMass

   people.umass.edu/partee/NZ_2006/Set Theory Basics.pdf

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   Where did the set theory notes come from?

   • These notes for a graduate course in set theory are on their way to be-coming a book. They originated as handwritten notes in a course at the University of Toronto given by Prof. William Weiss. Cynthia Church pro-duced the first electronic copy in December 2002. James Talmage Adams produced the copy here in February 2005.

   AN INTRODUCTION TO SET THEORY - University of Toronto Departmen…

   www.math.toronto.edu/weiss/set_theory.pdf

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   Who invented set theory?

   • Set theory was created by George Cantor (1845-1918) in the years 1874-1897. He was led to his ideas by certain problems in real analysis (Fourier series). In 1874 Cantor discovered that one cannot enumerate the real numbers by the natural numbers, showing that in nite sets come in di erent \sizes". It was a marvellous period of discovery.

   B1.2 Set Theory - University of Oxford

   www.maths.ox.ac.uk/system/files/attachments/SetTheoryHT18.pdf

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   What is the second primitive notion of set theory?

   • The second primitive notion of set theory is the notion of belonging. We write x ∈ X meaning ‘x belongs to the set X’, or ‘x is an element of X’ (Tipically we use capital letters to designate sets and small letters to designate elements of a set). Axiom 1a.

   Set Theory and Logic: Fundamental Concepts - MIT Mathematics

   math.mit.edu/~jhirsh/set_theory.pdf

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4. www.math.ucla.edu › notes › set_theory_notes_2Set Theory Notes - UCLA Mathematics

   www.math.ucla.edu › notes › set_theory_notes_2

   A PDF file of notes covering introductory set theory, including the axioms of ZFC, cardinality, forcing, and large cardinals. The notes also contain starred sections with optional topics and exercises.

   • File Size: 1MB

   • Page Count: 100

5. math.mit.edu › ~jhirsh › top_lectureSet Theory - MIT Mathematics

   math.mit.edu › ~jhirsh › top_lecture

   • Sets
   • Topological Spaces
   • Proposition 9.

   set is a collection of objects, called its elements. We write x 2 A to mean that x is an element of a set A, we also say that x belongs to A or that x is in If A and B are sets, we say that B is a subset of A if every element of B is an element of A. In this case we also say that A. Two sets are considered equal i A B and B A. contains B, and we wr...

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   Let X be a set. A topology on X is a collection of subsets of X, ie,

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   Let (X; d) be a metric space. Then X is Hausdor ogy. with the metric topol- Let (X; <) be a totally ordered set. Then X is Hausdor topology. with the order

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   • File Size: 212KB

   • Page Count: 15

6. math.mit.edu › ~jhirsh › set_theorySet Theory and Logic: Fundamental Concepts (Notes by Dr. J ...

   math.mit.edu › ~jhirsh › set_theory

   A PDF document that introduces the primitive concepts of set theory and logic, such as belonging, designations, sentences, quantifiers, and axioms. It also covers the basics of propositional logic, such as connectives, truth tables, and tautologies.

   • File Size: 218KB

   • Page Count: 8

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8. people.umass.edu › partee › NZ_2006Basic Concepts of Set Theory, Functions and Relations - UMass

   people.umass.edu › partee › NZ_2006

   1. Basic Concepts of Set Theory. 1.1. Sets and elements Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. The notion of set is taken as “undefined”, “primitive”, or “basic”, so we don’t try to define what a set is, but we can give an informal description, describe

9. www.maths.ox.ac.uk › attachments › SetTheoryHT18B1.2 Set Theory - University of Oxford

   www.maths.ox.ac.uk › attachments › SetTheoryHT18

   B1.2 Set Theory Lecture notes { HT 2018 Jonathan Pila Contents 1. Introduction 2. The language of Set Theory and the rst axioms 3. The Powerset axiom 4. The Axiom of In nity and the natural numbers 5. Recursion on the natural numbers 6. Arithmetic on the natural numbers 7. The axioms of Replacement and Foundation 8. Cardinality 9. Countable ...