document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935113>Question 935113</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is (R-{0},*) a group, how to prove it...<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568227 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=568227\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider, (R*,*) where R* = R - {0} IS a group.<BR>\n" );
document.write( "multiplication in R is associative, so remains associative on any subset of R.<BR>\n" );
document.write( "the product of two non-zero real numbers is again a non-zero real number, R* is closed under multiplication.<BR>\n" );
document.write( "1 functions as a multiplicative identity:<BR>\n" );
document.write( "for any NON-ZERO real number a, a*1 = 1*a = a.<BR>\n" );
document.write( "any non-zero real number a has a (unique) inverse, 1/a, with<BR>\n" );
document.write( "a*(1/a) = (1/a)*a = 1.  </SPAN>\n" );
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