117 0 obj 92 0 obj (\376\377\0004\000.\0003\000\040\000I\000n\000d\000u\000c\000t\000i\000o\000n) /Parent 140 0 R >j6j��>)��_u ��S��S�A���?�O�a�ѐ%��\�~$���BUc ��Ҕo���4���E�F��f1j�E[i4��;��6뼶�z����=Y�|�P$����k:���Y�\^B*�*�6�s01ho�M�ٰ�@��ȋu#`�ش�,[;� ��g��m#��. << /S /GoTo /D (section.3.2) >> 16 0 obj /Filter /FlateDecode 105 0 obj 113 0 obj (\376\377\0002\000.\0001\000\040\000B\000o\000o\000l\000e\000a\000n\000\040\000C\000l\000a\000s\000s\000\040\000O\000p\000e\000r\000a\000t\000o\000r\000s) << /S /GoTo /D (chapter.2) >> (\376\377\000B\000i\000b\000l\000i\000o\000g\000r\000a\000p\000h\000y) ��5W8�h��.^%�y9Q��-4Y�-�!���]/��z��C�����A�_#�FG����2�G�q�y��7mc����\f�9�Z��D�wN��K'�X ��Xր�ቾ�m �ވ5�AV���+D����9���(�٬���$�Ƃ�m�s#�k*�S16D��[�p'���>���%�p20YYɶQ2�d�8H�0�����1) 0�y��@�]ߪt������f������NgnM�%����+ෂ�E��:��jWgMkw�ně�M����'�7�^��5c���ZR���q��b+��M��д��NZ�-Z� "ٷ��;�i�ޥH� �i`葠78���F�,���Y��gϻq�7���E���u�]�?.�i��Kc-����S�ӡ� þ� ���{��n�'H{����s�s���I|���{�;:>���}�dǹd��ާr�S�4�����R�7�t��ܢD���qD�|�}q���i�-`��x��p����3�5w�_���"�������.�$��+�lH��S ��I��K^?�PmX�$\��� v�k 76 0 obj endobj >> endobj 32 0 obj (\376\377\0002\000.\0005\000\040\000I\000n\000f\000i\000n\000i\000t\000e\000\040\000B\000o\000o\000l\000e\000a\000n\000\040\000O\000p\000e\000r\000a\000t\000o\000r\000s) endobj 36 0 obj Historical Introduction 1 THE BACKGROUND OF SET THEORY Although set theory is recognized to be the cornerstone of the “new” mathematics, there is nothing essentially new in the intuitive idea of a set. This alone assures the subject of a place prominent in human culture. endobj endobj endobj endobj 20 0 obj The notion of set is taken as “undefined”, “primitive”, or “basic”, so we don’t try to define what a set is, but we can give an informal description, describe important properties of sets, and give examples. 16 0 obj << /S /GoTo /D (section.3.1) >> /ProcSet [ /PDF /Text ] 13 0 obj endobj This theory is interesting for two reasons. (\376\377\0004\000.\0005\000\040\000R\000e\000c\000u\000r\000s\000i\000o\000n) endobj << /S /GoTo /D (chapter.3) >> %���� 56 0 obj The set T = {2,3,1} is equal to S because they have the << /S /GoTo /D (section.3.7) >> endobj 85 0 obj endobj endobj 65 0 obj >> endobj << /S /GoTo /D (chapter.4) >> >> To Garth Gaudry, who set me on the road; To my family, for their constant support; And to the readers of my blog, for their feedback and contributions. 69 0 obj 21 0 obj This document contains the mathematical foundation of set theory. 104 0 obj 125 0 obj endobj endobj Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. endobj << /S /GoTo /D (section.5.1) >> /Length 479 endobj /Filter /FlateDecode ?� �3�v��["�%I��U�j��ͥ�9��:�.D�ǷY9�:h��V4o�5 Q~t۰ ���/@ (\376\377\0002\000.\0004\000\040\000S\000i\000n\000g\000l\000e\000t\000o\000n\000s\000\040\000a\000n\000d\000\040\000C\000l\000a\000s\000s\000\040\000P\000a\000i\000r\000s) n��l�-�?���?���;|��)����X.�g˱���fFz$���$������x]/O9B� @.�yz�� ,�Kó��U_��$p��C��gld.�$�p$�Е��cS,� @Mh��[i�^C}��k�a :�7 (\376\377\0003\000\040\000S\000e\000t\000s\000,\000\040\000R\000e\000l\000a\000t\000i\000o\000n\000s\000\040\000a\000n\000d\000\040\000F\000u\000n\000c\000t\000i\000o\000n\000s) endobj 48 0 obj endobj Notation. << /S /GoTo /D [133 0 R /FitH ] >> (\376\377\000I\000n\000d\000e\000x) << /S /GoTo /D (section.4.3) >> 13 0 obj endobj x��Zݓ۶�_�� �L���g�R�n��tҦ3�I�D�Ԑԝ忾�X�"i�tN�T4�̢�˯��?_}����$ᳫ�� �X̤Pa'�������"�:x������W�4~A� Goal is �o�u�SHi�ih� 4/�$��F�d�}� I\u9�+� ,: E�XD��c��b��z�}ӛ���z�6�'�MB�;Q�z4�����_��M�����!k ���5�ˉX1χb�\���g�a�\N��\}�1[���� �`C5@����g�M�!��j. gures in the development of set theory, Georg Cantor (1845{1918) and Richard Dedekind (1831{1916). >> endobj 80 0 obj /Resources 134 0 R endobj 61 0 obj 146 0 obj << endobj endobj endobj 120 0 obj We write S T to say the set S is a subset of set T. So, S T means 8x 2S (\376\377\0003\000.\0005\000\040\000R\000e\000l\000a\000t\000i\000o\000n\000\040\000A\000l\000g\000e\000b\000r\000a) Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. They are not guaran-teed to be comprehensive of the material covered in the course. (\376\377\0003\000.\0007\000\040\000M\000a\000p\000s\000\040\000a\000n\000d\000\040\000F\000u\000n\000c\000t\000i\000o\000n\000s) (\376\377\0004\000\040\000N\000a\000t\000u\000r\000a\000l\000\040\000N\000u\000m\000b\000e\000r\000s) 68 0 obj (\376\377\0002\000.\0006\000\040\000P\000o\000w\000e\000r\000\040\000C\000l\000a\000s\000s\000\040\000B\000u\000i\000l\000d\000i\000n\000g) 96 0 obj We will learn the basic properties of sets, how to de ne the size of a set, and how to compare di erent sizes of sets. 101 0 obj stream The elements of a set are the objects in a set. >> 136 0 obj << (\376\377\0001\000.\0002\000\040\000S\000p\000e\000c\000i\000a\000l\000\040\000C\000l\000a\000s\000s\000e\000s) <> 4.7 Embedding mathematics into set theory 4.7.1 Z 4.7.2 Q 4.7.3 R 4.8 Exercises 5. A set theory textbook can cover a vast amount of material depending on the mathematical background of the readers it was designed for. endobj Chapter 0 Introduction Set Theory is the true study of infinity. endobj /Length 3009 >> endobj Selecting the material for presentation in this book often came down to deciding how much detail should be provided when explaining concepts and what constitutes a reasonable logical gap which can be independently filled in by the reader. 44 0 obj :4/}gښ�^�(s�ݝ嫰�Лڀ�C�dm^���+8*(�(��t�G���cn�~����,ȡ�l��XR�dVR�ʞi�[�֙/p����s�^�1��a�|�u�D�������MY�{�E)X}ֽ�j�k�ree�~�i��������2xZ��x�'�AQ�זy����/L�t$��6���U(b���g��yt���ԲRT6^�^���e��m�^筛qm�V�]Yvm��3T�4�z�V� F�MN3�.

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