document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=975490>Question 975490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a number set has no supremum or it has a supremum which is infinity . does the two statement same ???  if a set is S={1}  what will be it's supremum and infimum also show it's all upper bounds and lower bounds too. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597261 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=597261\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "A set cannot have a supremum that is infinity.  A supremum is a number, whereas infinity is not.  If S = {1}, and S is a subset of T, then T must contain the element 1, and then 1 is the smallest element of T that is greater than or equal to all elements of S.  Supremum and Least Upper Bound being equivalent terms, 1 is also the Least Upper Bound.  Similarly, 1 is the infimum or greatest lower bound.\r<BR>\n" );
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document.write( "Note that if set S was defined as all real numbers in the open interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0\ <\ x\ < 1\"> and T is the set of all real numbers, neither the supremum of S nor the infimum of S are actually elements of S.  Here the supremum is 1 and the infimum is 0.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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