document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166868>Question 1166868</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the definition of ⋆ does give a binary operation on the set. In case that ⋆ is not a binary operation, state the property it fails to satisfy and give a counterexample.\r<BR>\n" );
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document.write( "a). Let S = ℕ, define ⋆ by a ⋆ b=c, where in c is the largest integer less than the product of a and b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791440 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "The post / (the condition) is &nbsp;FATALLY &nbsp;INCOMPLETE, &nbsp;since it does not determine what the set &nbsp;N &nbsp;is.\r<BR>\n" );
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document.write( "The standard designation for the set of integer numbers is &nbsp;Z;\r<BR>\n" );
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document.write( "so, &nbsp;based on the post, &nbsp;the set of numbers in this problem is not &nbsp;Z;\r<BR>\n" );
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document.write( "then &nbsp;WHAT &nbsp;it is ?\r<BR>\n" );
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document.write( "It is a typical case at this forum, &nbsp;when the person who creates / (composes) &nbsp;the problem,\r<BR>\n" );
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document.write( "does not know the subject and does not know &nbsp;WHAT &nbsp;he &nbsp;(or she) &nbsp;writes about and how to write it correctly.\r<BR>\n" );
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document.write( "------------\r<BR>\n" );
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document.write( "From Wikipedia, &nbsp;the free encyclopedia  \r<BR>\n" );
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document.write( "https://en.wikipedia.org/wiki/Binary_operation#:~:text=In%20mathematics%2C%20a%20binary%20operation,operands)%20to%20produce%20another%20element.&text=Examples%20include%20the%20familiar%20arithmetic%20operations%20of%20addition%2C%20subtraction%2C%20multiplication.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "    In mathematics, a binary operation or dyadic operation is a calculation that combines two elements (called operands) \r\n" );
document.write( "    to produce another element. More formally, a binary operation is an operation of arity two.\r\n" );
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document.write( "    More specifically, a binary operation on a set is an operation whose two domains and the codomain are the same set. \r\n" );
document.write( "    Examples include the familiar arithmetic operations of addition, subtraction, multiplication. \r\n" );
document.write( "    Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication and conjugation in groups.\r\n" );
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document.write( " </SPAN>\n" );
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