/Contents 9 0 R stream 13 0 obj << This is the amount of set theory that everyone with an interest in matters mathematical should know. The notion of set is taken as “undefined”, “primitive”, or “basic”, so we don’t try to define what a set is, … 1. >> It’s probably a good idea to look through the supplement at the start of the course, but completing many Any formal theory starts with the speci cation of its language. xڽYYo��~�_��� ���l^3@ /�A��l2J�B(�e1�CKRc+�>U]�K�lOf������ꮖ�_����,ֻE�U,�/���o�w���-W��9�������v�˥�����+x��m�U%�=Jڽ)�6�&9Q�˕t�K�d��| Iw}��2�N��DQ�T@�������������?ֿ��C4�u\$/\B+�C� /Resources 1 0 R Intuitively, a set is a collection of all elements that satisfy a certain given property. This brief document summarizes what is required. >> stream /Resources 7 0 R /MediaBox [0 0 595.276 841.89] In other words, we might be tempted to postulate the following rule of formation for sets. %PDF-1.5 /Filter /FlateDecode 1 Elementary Set Theory Notation: fgenclose a set. JN��A�r�=? /ProcSet [ /PDF /Text ] f1;2;3g= f3;2;2;1;3gbecause a set is not de ned by order or multiplicity. Why Axiomatic Set Theory? ��w�P�Գ432SIS043�333W076�304WIQ����Ԍ ��r � �: 1.1. /Filter /FlateDecode � /Length 56 %}��\��@�R�]n 8 0 obj << /MediaBox [0 0 595.276 841.89] ��zP�ؓ�����4�����ͶޱYƝ[�u�ɯ��?���R�O�\�"��C�{��]�SK����c�z3���R\$ Those with a special interest in set theory itself are encouraged … /Parent 6 0 R 1.2 The language of the theory Zermelo{Fraenkel set theory with the Axiom of Choice (ZFC) is just one formal theory among many. /Type /Page Basic Concepts of Set Theory. Elements of Set Theory This course assumes you (the student) are familiar with basic set theory. x��Y�r�6��+��K. The theory with axioms 1.1–1.8 is the Zermelo-Fraenkel axiomatic set theory ZF; ZFC denotes the theory ZF with the Axiom of Choice. /Length 1002 /Parent 6 0 R /Contents 3 0 R >> endobj ]�3���]� �X7����9�.�Ω:u#�G�SS��9�%���C����H��1k�D� O�d[�lLK(V �X����`K��q�������"���tX� ��v��z%��}�أ~9f�G����s߾m���զ� K��ODM�9���%K��\$6S@͉�3S�\$�����^���`��1�l��=O��L���ߒ\p� 6Ƕ_ Ho)��V\$�i�6V,�����c��E��k_ ���-��l�ඊX6]��/fdiZ���YĖ�u����F�U�W�j�u����TU��XȆ�w�'�kycZ�p /ProcSet [ /PDF /Text ] 2 0 obj << endstream >> endobj endstream ]�( �b���Wh�_ZW�#��Xؐ}��onhgR�s�0&P��l � ��/(����8�(~l��tA����BV\V` �Kٹ���U�5��>����J�����*8����(�:[�bL������� A�Qjxgہ|�W��B. 1. x�s /Type /Page /Font << /F8 10 0 R >> They look like they could appear on a homework assignment in an undergraduate course. stream >> /Length 2313 x�%���0�~��D�&v즌 ��9b#H-Em��D��-w���( � Here are three simple statements about sets and functions. stream endobj >> endobj %���� For any two sets X and Y, either there is a one-to-one function from /Length 132 1g�5�U8;:�)��� tbB�.�r������q�bN�x� �ΐ�C2��#�*���[^�D�x��#? 9 0 obj << %PDF-1.5 endobj 1 0 obj << 3 0 obj << Elements of Set Theory number 2);the set of customers who came into the hardware store during a givenday and the set of cus-tomers who left it during that same day (assuming of course that all indecisive customers, whateverthe time of their entrance into the store, will be … Academia.edu is a platform for academics to share research papers. %���� ZFC belongs to a class of formal theories known as rst order theories. f0;2;4;:::g= fxjxis an even natural numbergbecause two ways of writing /Filter /FlateDecode >> endobj 3 0 obj << @���zo��DR��H�Ծ�2Z�_�x Sets and elements Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. >> Because the fundamentals of Set Theory are known to all mathemati-cians, basic problems in the subject seem elementary. A course in axiomatic set theory might reasonably cover the first six or seven chapters, omitting Chapter 5. 7 0 obj << /Filter /FlateDecode /Font << /F15 4 0 R /F16 5 0 R >>