Math 1010 On Line The Real Number Line University Of Utah
The real number system can be visualized as a horizontal line that extends from a special point called the Origin in both directions towards infinity. Also associated with the line is a unit of length. The origin corresponds to the number 0. A positive number x corresponds to a point x units away from the origin to the right, and a negative number -x corresponds to a point on the line x units away from the... All of this is illustrated in the above Figure. We said that the number corresponds to a point on the real number line, but actually there is no useful distinction between a real number and its corresponding point on the real number line.
Hence we may also say that a real number is on the real line, and a point on the real number line is a real number. We say that a number x is greater than a number y, in symbols Similarly, we say that x is less than y, in symbols Now get ready for a bit of convoluted logic that often confuses students in Math 1010. �S0ϫϘ�X�k &�H�����t��K��(";�r��T R ���G���:�T1��L�(~x�M߈�ɕ������>R�3i�DDJ�� l�$��� ��n��5�uR�][�w8fJG��l0�p��&U���R �c���q��DZh���v�7���Q>��+9c>;}����Q7s�6D�W�mc^W�dL���p����GҖ�c�K�Jɇr��ꠖ�QԲuF���T�n,�CU�&�R���mxE��῾�MMл��B{��/ ����jo\S)"�-W�/N�"x)4I��g2�+e�No֫#�x9T�L�3o��u�6ov�I�-�"i����n ��j���P$;o�T��8R���KB��7O���J������ ��P�Y��hB ��٠4f� J�B>�x�N(����3PΒe^�Ұ��ffRܹ��@�̜�Ұ� J��( D�R�uJ��.(�9���.(m_:�9(����%(��~�R�hAV�g��Zw"-K��Bi�?���4��C*��;|���.@)�xJ��.( g�(Z�4��sP 8]��� J�P��,/@i��(e�3�ya;����O0n��_�b�,��ޓp�����7����ÿ���G��o� �R���i����u�o�#�_�j��������/^��Z���f�������o;~a|�����ۿ�����3~�'�x%Dbs Jf��Aʳ&��*�v��M_;͗2W��]z�ڥn�@��M��~�lB�%k��9qy~Q���ft���>��1'(���\��X�Y}��1^y��[i�(X�8���٣�j���T��N�F���FZ;��W�g���vIU٥��R}�(�sS�vL9�t&Jm�ԣ�_���͐���ൈd���1a(�� J� e66i5��}��1^�xv��v�Ƭ��GϜ�Jk��3�=�����uR�D�L�'Ù��)S�����>-�x�B�?"0��z��Δ.�6�= �>�f�����ʩ�d��H[���0��y�gF�P�l��/88˲�qe�u<+�p��@����@�V��+W�Idko����eT��?�J�Ηp�O_5��Vs�;���2�1A�k��rP}�f�d;�"ue[}v����"f�1c���H"�u�\���������?���*�?X ��� ~��Td���%[�>�>��?�;����A}j��(�������u>e�tyiĶ�>e��E��� ����-���v����Y\�m'�1�K��=�IJ`1u��Z���|�5�؍k��,�����]~�5�u��������ŵ��-����5{�v���e� u4����Ծ�Z�����'\;E2G����\ �]�k�� ���pm�h�8�5�p ���z��jG�נ&���3.����>��`ߢ�����[Az�`�������F�v���P����n�#6�H�M(qyr�W[�_J�������p�T�%k_)����P�YA���c�(����.�ݞ�s��1�A��<�c"T�>-�| �s<����a���ܕ�uT�r��7�������&:��^k ǖ��(��|Vb�Ɣ� rFM�$��p0zIr��&��ؕc26IT��^-���q8��[>]�j]����-fM@',ϛ�N�\j҃Y�?7���;Lo�E�)O�j�SlR?�So8S2(4e/�A�P�_�v]-vx�*р��H���� �q�_�K�,�u������O"^_��c�;�?�u���>�aݤ�����ɫ�־�?z��\��XøE�O�9����x��r��ɔCV�}�G���|��IK���� �[`�... t���s��v���"�@�j��v������S�FN,���@�O�� �� �]6���BZ�"tf}����d�&- �.o���1>� c��3�z#U�,��}� �7����S��ݗ�<5�_�^N�>���� *(c�Q�$̸dza��2�K�W�B [�1�1��Loz�`z�l���e@�� ��B�k��enL/X�4������ �Eӻ鳦7"�_2���jitm��� �5��k��V�HΙ�`�������4��u���>��.�^0�iz#]��~az� c�i�`z����]���`z���� �W��7���W������ιZ ,��U @o�z8����'��� \�/�~��?ra�U����\��?��X7*��\�5Z��Uo��_<"3�9ݧ�%��eUD��(#B�Dno�x��e�{=� d�Ť�x��x�h� �8���R��;�q{Ťqqm�c�Ѵ� �$�H����B�����['�>\ u�\LH�jDU�Ț��d��І��ՍN�~N��l�K���ĪfDȺ��GRou���L� Y J�.��R'V$��[C !y�T����Gȷ�S@JF�%��f�b#v�@%B�'B����:�QB��%���p���/�ZT� �J=�}�Y��Z����P1�*�o<#Q�����|� d�A�2:�Yx�U�:^kJ����,���풘�{$@hTY�0 K$OH�l�P0��B�Js8��Q�ſߪ��C����Y�%��MzY�$f�/gK[(:�[M�=�������������φ�Ե�Q*O�Td�=�W٣Dz��g{��WأP��=��;���}a�� f��}~k���{���G`�t�=����Gѡ/�XaW��GG����ū�Q�:c�������#��*{�����Q���朱G�u�=�|}i�"]W�#�:c�bs��G| ��������Џ�z=)�x�GM+�A0,��>q\��C�nî��P��|��*KI?j�� k���x}o�pxO�Ow'=a��%�����f�jk��f�i+�����s>���T��n�\��.Y� 9��ǎ�n�a�O|��n��11~{��MHX��¢���aH���@D@�2�z{ӓ}^}Ϯۛ��ܝ��s��$/�����q��iH�`w����gNd���z��TC����P∜��;ɬ%N� 4>H������* eo`��X���M�<��3�ƧE�l�����DwF)a���]� �x���@�I��h�i.�x��t��y����{�j��F��ē�߂�^o�5k`�w=5ok�O...
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An example of an identity is The focus on this page, however, is on equations that are true only for some values of the variables. There may be several such variables, but to begin with we assume there is only one, and we usually call it . Figuring out for which values of an equation is true is called solving the equation. A value of that makes the equation true is called a solution of the equation. For example, the equation
The fundamental principle of equation solving is based on the fact that after applying the same operation on both sides of the equation the solutions of the original equation are also solutions of the... Think of the equation as one of those old fashioned scales that balance an initially unknown weight with a combination of known weights. If everything is in balance and you do whatever you do on both sides everything will still be in balance. Simply put, the fundamental principle of equations solving is To solve an equation figure out what bothers you the most at the moment and get rid of it by applying a suitable operation on both sides of the equation.
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The Real Number System Can Be Visualized As A Horizontal
The real number system can be visualized as a horizontal line that extends from a special point called the Origin in both directions towards infinity. Also associated with the line is a unit of length. The origin corresponds to the number 0. A positive number x corresponds to a point x units away from the origin to the right, and a negative number -x corresponds to a point on the line x units away...
Hence We May Also Say That A Real Number Is
Hence we may also say that a real number is on the real line, and a point on the real number line is a real number. We say that a number x is greater than a number y, in symbols Similarly, we say that x is less than y, in symbols Now get ready for a bit of convoluted logic that often confuses students in Math 1010. �S0ϫϘ�X�k &�H�����t��K��(";�r��T R ���G���:�T1��L�(~x�M߈�ɕ������>R�3i�DDJ�� l�$�...
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An Example Of An Identity Is The Focus On This
An example of an identity is The focus on this page, however, is on equations that are true only for some values of the variables. There may be several such variables, but to begin with we assume there is only one, and we usually call it . Figuring out for which values of an equation is true is called solving the equation. A value of that makes the equation true is called a solution of the equatio...