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</html>";s:4:"text";s:12021:"Suppose {x n} is a convergent sequence which converges to two different limits x 6= y. %���� x��َ���}�B�'�ðor~ȱIl� � �~�J��)��������橖4cO�$/R���uuUu1Y�-�ş�������ퟘY0���v���nj��I�8�lq�Z|��jms}#�������m],��~�/����o�Z�$Β�!�&D��lq�U,DF�n7���7\��$�\Ȩ(�y�uU�KK��Ə]V���[�Tk�����xY���g������r��f�x�/��lh��ęJ���a������6���b���?�����%5ڦ�t�"���,*��n��p��-���р#�Ȋ��u�Mh�Lé5b�y�A\�� The di cult point is usually to verify the triangle inequality, and this we do in some detail. �`P���i�w?�[����>rbWg�Y�vhl7��n*��O�K:}��vR�!�9#�]������l��d�i�PN��VpV�#uDp��ݳ�6|]�M�[��K�A1���J(�F�q@ H ��!/�T-c�SZ�$����ZKr��Z� �|.����ĭ�?�����F��b��/���$��h���m�WE���/AI��E�� |i
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���,i�m�^ �r����a��G27��ьi��~�9?��>gI�ä�d�p҆ (i) V is a R -vector space: If either x = 0 or y = 0 the inequality is obvious. The set of real numbers R with the function d(x;y) = jx yjis a metric space. Then ε = 1 2d(x,y) is positive, so there exist integers N1,N2 such that d(x n,x)< ε for all n ≥ N1, d(x n,y)< ε for all n ≥ N2. >> The fact that every pair is "spread out" is why this metric is called discrete. x��\I��6��W���. "'F�9��,�=`/��Ԡb��o����蓇�. k|���*Y�L���ik}��>)Xf̍LL.w�^�?\/2�[���Z/R}��p�����{-A��2�#��πe�F�np�����XYR1`q��,��7Aػ�|�\�C��~ao;�(�DE�3/���p���ӣ?�P!�L����HH
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