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[數學]one more question on "Groups"
由 jocelyn 於 星期五 十月 06, 2006 3:46 pm
#ed_op#DIV#ed_cl#1. Let S1={X^2 : X is real number} and S2= {X^2 : X is real number, X not equal to 0}.#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#a) Show that the binary operations + ,#ed_op#SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 新細明體; mso-font-kerning: 1.0pt; mso-bidi-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl#．#ed_op#/SPAN#ed_cl#on real number restrict to binary operations on S1 and on S2.#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#b) Which of the structures (S1,+), (S2,+),(S1,#ed_op#SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 新細明體; mso-font-kerning: 1.0pt; mso-bidi-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl#．#ed_op#/SPAN#ed_cl#),(S2,#ed_op#SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 新細明體; mso-font-kerning: 1.0pt; mso-bidi-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl#．#ed_op#/SPAN#ed_cl#) is a group? For each case for which it isn't a group, explain which group properties fail to hold.#ed_op#/DIV#ed_cl#