document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=259928>Question 259928</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Why is every irrational number a real number but not every real number is am irrational number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #191397 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=191397\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The set of irrational numbers are real since they can be represented as decimal numbers. The decimal patterns don't repeat (or don't have a clear pattern), but they are still real numbers. So if you have an irrational number, it is also a real number.\r<BR>\n" );
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document.write( "On the other hand, if you have a real number, you aren't guaranteed it's irrational. Take for example the number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This number is rational (as opposed to irrational) and it is real. So not all real numbers are irrational. </SPAN>\n" );
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