document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=698728>Question 698728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Yes, Hi. I need to show the conjecture is false by finding a counterexample in the following statement:\r<BR>\n" );
document.write( "\n" );
document.write( "The product of any two consecutive integers is positive.\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #430998 by </B><A HREF=/tutors/aboutme.mpl?userid=Positive_EV><B>Positive_EV(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Positive_EV><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=Positive_EV><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=430998\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A counterexample is any example of two numbers which shows the statement is false. Here, that is a set of integers that results in a product that is not positive. For this problem, remember that the product of any number times 0 equals 0. Since 0 is an integer, and it is not positive, if 0 is one of the numbers the product will not be positive.<br>\r<BR>\n" );
document.write( "\n" );
document.write( "-1 and 0 is one such counterexample. 0 and 1 is another. I think these are the only two counterexamples, since the product of two negative numbers is positive, and the product of two positive numbers is positive. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );