sets lecture notes pdf

Cynthia Church pro-duced the ﬁrst electronic copy in December 2002. For those of you new to abstract mathematics elementary ��8SJ?��M�� Y ��)�Q�h��>M��WU%qK�K0$�~�3e��f�G�� =��Td�C�J�b�Ҁ)VHP�C.-�7S-�01�O7��ת��L:P� �%�",5�P��;0��,Ÿ0� USMLE Step 1 Lecture Notes 2020: 7-Book Set PDF Free Download USMLE Step 1 Lecture Notes 2020: Anatomy PDF Free Download Table of Contents. - Georg Cantor This chapter introduces set theory, mathematical in-duction, and formalizes the notion of mathematical functions. Example: • {1,2,3} = {3,1,2} = {1,2,1,3,2} Note: Duplicates don't contribute anythi ng new to a set, so remove them. A set is said to contain its elements. James Talmage Adams H��Kk�0��w)A��#�lR()Ի��t��Cȿ�vF��B��p}�{�I��A0>Ԡ�jE.��8Sh��s4Xx�Ҝ�1`�Fǘ�� 4 CS 441 Discrete mathematics for CS M. Hauskrecht Equality Definition: Two sets are equal if and only if they have the same elements. 0000001785 00000 n 0000004758 00000 n Let xbe arbitrary. 0000003957 00000 n Ling 409, Partee lecture notes, Lecture 1 September 7, 2005 p. 2 Examples: the set of students in this room; the English alphabet may be viewed as the set of letters of the English language; the set of natural numbers1; etc. So sets can consist of elements of various natures: people, physical objects, The following theorem and examples will give us a useful way to deﬁne closed sets, and will also prove to be very helpful when proving that sets are open as well. LECTURE NOTES ON SETS PETE L. CLARK Contents 1. The left hand side is a subset of the right hand side. Deﬁnition. 0000055893 00000 n H��TMo�0��W�і6��#�nH�� C�z�Em�ڤB�{��J��9�؞�7��˶8k[M��U�o�!�ogj/�#ﴨ��}(��'G��$M�P�}�Rt;�RJKm_D�ߋkv��N6�R�a�K�\Pw��݆�s�k��l�%y��p�k��e7倉.��m�1�IƂ>u�9J��1�!��m?� [׊J%�U��w��׮m.��F0�zTm�� &� �,�`��D��UF(++|��Ҫ��Y�"R2+��Lm� F�0n�u�D�e��$n��ˊ� 2�,��ml�qo��^��XˬdDWn߲R��%@�@:��a3O�jF㊮��b��.��U�yd��Ϙ�9��g}y`,��ZBl^��0��RϨc��>��4�shy7�qB|n8Y�!/Q�6ё��AG�kj�͑Y��p%h�EN�� &r�r=��,�B�tj8�f9CZ4��G��=Tw�/\6��$"�N�7�~��u�35��Е��~�^��J��~~�i �T�H�K:6�r�j/�>*��^Ii�Jr�I��i"�o�t�#�T��(*��R�)�U��3��2_"o�1/��kD�m�K�Nu��j垾M�A5w��c�mB�^�b9��Q��B��q��uӸkQ�u�Ǳg��h�S� �ۛ endstream endobj 47 0 obj 488 endobj 48 0 obj << /Filter /FlateDecode /Length 47 0 R >> stream We'll give a couple of di erent examples here. 93 0 obj <>stream A set can be deﬁned by simply listing its members inside curly braces. Introducing Sets 1 2. 36 0 obj << /Linearized 1 /O 38 /H [ 1300 485 ] /L 209425 /E 154156 /N 10 /T 208587 >> endobj xref 36 43 0000000016 00000 n … Example 1.3.4. 0000001300 00000 n Here’s the complete overview of USMLE Step 1 Lecture Notes 2020: 7-Book Set PDF: Kaplan Medical’s USMLE Step 1 Lecture Notes 2020: 7-Book Set offers in-depth review with a focus on high-yield topics in every discipline—a comprehensive approach that will help you deepen your understanding while focusing your efforts where they’ll count the most. 2. Asetis a collection of abstract objects. Below is the complete table of contents which you will be able to access inside USMLE Step 1 Lecture Notes 2020: Anatomy PDF: Section I: Early Embryology and Histology: Epithelia Chapter 1: Gonad Development Chapter 2: Week … 0000010658 00000 n Theorem 1.1. 0000005345 00000 n 0000096302 00000 n We present two families of such operators, namely OWA operators and quasi-arithmetic mean operators, and cover … �u�Q��y�V��|�_�G� ]x�P? The right hand side is a subset of the left hand side. %%EOF LogicalEquivalences.pdf Let's take a quick look at this Cheat Sheet. Proving Set Equivalences Recall that to prove such an identity, one must show that 1. 0000001764 00000 n A … 0000005366 00000 n 0000008932 00000 n Lecture 3 covers the triangular norm aggregation operators, providing fuzzy set intersection and union operators. 0000006026 00000 n H�[}K�`G��2/�m��S�ͶZȀ>q��y��>`�@1��)#��o�K9)�G#��,zI�mk#¹�+�Ȋ9B*�!�|͍�6��-�I��v��f":��k:�ON��r��j�du��6Ѳ�� h�/{�%? 3. 0000003690 00000 n 1In the case of set theory one could dispute this. Ling 409, Partee lecture notes, Lecture 1 September 7, 2005 p. 2 Examples: the set of students in this room; the English alphabet may be viewed as the set of letters of the English language; the set of natural numbers1; etc. 0000004779 00000 n In this blog post, we are going to share a free Kaplan USMLE Step 1 Lecture Notes 2020 PDF: 7-Book Set PDF Download using direct links. 0000003177 00000 n 0000012622 00000 n Cartesian Products 11 1. The material in these notes is introductory starting with a small chapter on linear inequalities and Fourier-Motzkin elimination. Set Theory \A set is a Many that allows itself to be thought of as a One." 77 0 obj <> endobj 0000139607 00000 n 83 0 obj <>/Filter/FlateDecode/ID[<7699FE2A76498BA3504AB9257FEAFED9>]/Index[77 17]/Info 76 0 R/Length 53/Prev 67195/Root 78 0 R/Size 94/Type/XRef/W[1 2 1]>>stream 0000121046 00000 n Power Sets 5 4. De nition 1.2 (Union). The order of the elements in a set doesn't contribute 1�t�1��@�DD��%�$�((��Ȓ� 2�q�PZ��Yy�Vb-�Q�]N2�d|�p�L߁X��$��p�� F��@�]� w��n ��ӹ,g兟s}�0�#�B�!��.c*��J�4{ ��z( endstream endobj 78 0 obj 372 endobj 38 0 obj << /Type /Page /Parent 33 0 R /Resources 39 0 R /Contents [ 46 0 R 48 0 R 50 0 R 52 0 R 60 0 R 64 0 R 66 0 R 68 0 R ] /MediaBox [ 0 0 595 842 ] /CropBox [ 0 0 595 842 ] /Rotate 0 >> endobj 39 0 obj << /ProcSet [ /PDF /Text ] /Font << /TT2 41 0 R /TT4 42 0 R /TT6 53 0 R /TT8 54 0 R /TT10 57 0 R /TT12 61 0 R >> /ExtGState << /GS1 70 0 R >> /ColorSpace << /Cs6 44 0 R >> >> endobj 40 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 34 /FontBBox [ -558 -307 2000 1026 ] /FontName /FFCPFL+TimesNewRoman,Bold /ItalicAngle 0 /StemV 133 /FontFile2 72 0 R >> endobj 41 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 233 /Widths [ 250 0 0 0 0 0 0 0 333 333 0 564 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 278 564 564 564 444 0 722 667 667 722 611 556 722 722 333 0 722 611 889 722 722 556 722 667 556 611 722 0 944 0 722 0 333 0 333 0 0 0 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 480 200 480 0 0 0 0 0 0 0 1000 0 0 0 0 0 0 0 0 0 0 0 333 333 444 444 0 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 444 ] /Encoding /WinAnsiEncoding /BaseFont /FFCPAJ+TimesNewRoman /FontDescriptor 43 0 R >> endobj 42 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 148 /Widths [ 250 333 0 0 0 0 0 0 0 0 0 0 250 333 250 0 0 0 0 0 0 0 0 0 0 0 333 0 0 0 0 500 0 0 667 722 722 667 611 0 0 0 0 0 0 0 722 0 0 0 722 556 667 0 0 1000 0 0 0 0 0 0 0 0 0 500 556 444 556 444 333 500 556 278 333 0 278 833 556 500 556 556 444 389 333 556 500 722 0 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 500 ] /Encoding /WinAnsiEncoding /BaseFont /FFCPFL+TimesNewRoman,Bold /FontDescriptor 40 0 R >> endobj 43 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 34 /FontBBox [ -568 -307 2000 1007 ] /FontName /FFCPAJ+TimesNewRoman /ItalicAngle 0 /StemV 94 /XHeight 0 /FontFile2 71 0 R >> endobj 44 0 obj [ /ICCBased 69 0 R ] endobj 45 0 obj 702 endobj 46 0 obj << /Filter /FlateDecode /Length 45 0 R >> stream 0000013583 00000 n De nition 1.1 (Subset). 0000003978 00000 n h�bbd``b`�$�C�`��@�+#��#1�Ɗ *� 0 In mathematics, the notion of a set is a primitive notion. So sets can consist of … 0000002411 00000 n 0000078392 00000 n �M�,� S)��r�� 0000011655 00000 n The lectures 4–7, we cover averaging aggregation operators, that is, the mean function in fuzzy logic. Because A Bif x2Athen x2B Because B Aif x2Bthen x2A Hence, x2Ai x2B, thus A= B. Ling 310, adapted from UMass Ling 409, Partee lecture notes March 1, 2006 p. 4 Set Theory Basics.doc 1.4. The objects in a set are called the elements, or members, of the set. 0000006005 00000 n Proof. (Notes by Dr. J. Santos) A.1. The aim is to show Cantor’s discoveries were profound, but even so, the main in uence of set theory on the rest of mathematics was to enable simple constructions of great generality, like cartesian products, quotient sets and power sets, and this involves only very elementary set theory. The theory of convex sets is a vibrant and classical ﬁeld of modern mathe-matics with rich applications in economics and optimization.

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