/ProcSet [ /PDF /Text ] /Font << /F8 10 0 R >> endstream 1 Elementary Set Theory Notation: fgenclose a set. x�s This brief document summarizes what is required. /Filter /FlateDecode This is the amount of set theory that everyone with an interest in matters mathematical should know. In other words, we might be tempted to postulate the following rule of formation for sets. The notion of set is taken as “undefined”, “primitive”, or “basic”, so we don’t try to define what a set is, … 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��| Iw}��2�N��DQ�T@�������������?ֿ��C4�u$/\B+�C� � 1g�5�U8;:�)��� tbB�.�r������q�bN�x�
�ΐ�C2��#�*���[^�D�x��#? /Length 56 >> endobj 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. /Contents 3 0 R /ProcSet [ /PDF /Text ] stream 1. Those with a special interest in set theory itself are encouraged … endobj A course in axiomatic set theory might reasonably cover the first six or seven chapters, omitting Chapter 5. Intuitively, a set is a collection of all elements that satisfy a certain given property. /Type /Page >> Sets and elements Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. >> endobj /Parent 6 0 R x�%���0�~��D�&v즌 ��9b#H-Em��D��-w���( � 8 0 obj << Because the fundamentals of Set Theory are known to all mathemati-cians, basic problems in the subject seem elementary. Elements of Set Theory This course assumes you (the student) are familiar with basic set theory. 1 0 obj << /Font << /F15 4 0 R /F16 5 0 R >> Why Axiomatic Set Theory? >> endobj /Resources 7 0 R /MediaBox [0 0 595.276 841.89] 7 0 obj << 1.2 The language of the theory Zermelo{Fraenkel set theory with the Axiom of Choice (ZFC) is just one formal theory among many. 9 0 obj << JN��A�r�=? /Resources 1 0 R /Length 1002 /Type /Page Here are three simple statements about sets and functions. ]�(
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� �: >> endobj /MediaBox [0 0 595.276 841.89] endobj It’s probably a good idea to look through the supplement at the start of the course, but completing many ZFC belongs to a class of formal theories known as rst order theories. 1.1. %���� They look like they could appear on a homework assignment in an undergraduate course. For any two sets X and Y, either there is a one-to-one function from %}��\��@�R�]n %PDF-1.5 >> 13 0 obj << /Contents 9 0 R f0;2;4;:::g= fxjxis an even natural numbergbecause two ways of writing 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 … /Parent 6 0 R ]�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�
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