document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1048488>Question 1048488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that the set is infinite by placing it in a one to one correspondence with a proper subset of itself. give the general term of the original set and show its pairing with its proper subset<BR>\n" );
document.write( "{4,16,64,256,1024} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #664081 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=664081\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The infinite set would be the set of all positive integers.\r<BR>\n" );
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document.write( "Its proper subset that would have a one-to-one correspondence with itself is the subset of all powers of 4 (using positive exponents).\r<BR>\n" );
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document.write( "The one-to-one correspondence is given by the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28n%29+=+4%5En ALIGN=MIDDLE  ALT=\"f%28n%29+=+4%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where n = 1,2,3,4,5,... </SPAN>\n" );
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