document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=671930>Question 671930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider a set, S, whose cardinality is greater than the cardinality of the real numbers. Write in words how you woud go about constructing a set that has greater cardinality than S. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #417744 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=417744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let T be a set. Show that |T|> |S|. Let n = |S| and likewise let m = |T|. Note that the cardinality of the reals is uncountably infinite, then the cardinality of S is also uncountably infinite. We want to construct a set such that for some element e, that is not in S, it exists in T. Then there is no longer a one-to-one correspondence between S and T. Since T has one more element than S, then |T| > |S|. </SPAN>\n" );
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