0000002189 00000 n 0000008953 00000 n De ning a set formally is a pretty delicate matter, for now, we will be happy 0000011655 00000 n 0000012643 00000 n 0000006827 00000 n ]Z��. 0000009963 00000 n In this chapter we will outline the background needed for a course in abstract algebra. June 2011. Dedekind was the rst to introduce 510 Cover design, Layout design and Typesetting by Claire Ho. Subsets A set A is a subset of a set B iff every element of A is also an element of B.Such a relation between sets is denoted by A ⊆ B.If A ⊆ B and A ≠ B we call A a proper subset of B and write A ⊂ B. 0000016260 00000 n ���E�]gZ��I�����5�����A� 0000013583 00000 n 0000078392 00000 n SET A. 0000007797 00000 n 0000012622 00000 n In this chapter we will outline the background needed for a course in abstract algebra… Solution - Pure Mathematics for Beginners: A Rigorous Introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra … H���Kk�0���w)A��#�lR()Ի��t����Cȿ�vF���B���p}�{�I����A0>Ԡ�jE.��8Sh������s4Xx�Ҝ�1`�Fǘ��� 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 Ling 310, adapted from UMass Ling 409, Partee lecture notes March 1, 2006 p. 4 Set Theory Basics.doc 1.4. 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