document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=544773>Question 544773</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a is a irrational number and b is an rational number, prove that either (b &#8722; a) or (b + a) is<BR>\n" );
document.write( "irrational. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #355218 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=355218\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Both must be irrational. Suppose that b-a is, on the contrary, a rational number r. Then a = b-r, contradiction because the sum/difference of two rational numbers is always rational (another way we can say this is that addition and subtraction are closed under rational numbers). The same logic applies to b+a = r. </SPAN>\n" );
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