document.write( "Question 519318: my teacher gave us an extra credit question which was:
\n" ); document.write( "given: A=B
\n" ); document.write( "prove: B=26\r
\n" ); document.write( "\n" ); document.write( "he did half of it like this\r
\n" ); document.write( "\n" ); document.write( "1. A=b 1. given
\n" ); document.write( "2. a*a=b*a 2. multiplication postulate of equality
\n" ); document.write( "a^2=ba
\n" ); document.write( "3. a^2-b^2=ba-b^2 3.multiplication postulate of equality.
\n" ); document.write( "(a+b)(a-b)/(a-b)=b(a-b)/(a-b)
\n" ); document.write( "4.(a+b)=b
\n" ); document.write( "5. b+b=b\r
\n" ); document.write( "\n" ); document.write( "the extra credit is to tell him what he did wrong and why?
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Algebra.Com's Answer #345533 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Here are all the steps to the bogus proof that 2 = 1.  I put in\r\n" );
document.write( "a few omitted steps.\r\n" );
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document.write( "1. a = b                 1. given\r\n" );
document.write( "2. a·a = b·a             2. multiplication postulate of equality\r\n" );
document.write( "   a² =  ba\r\n" );
document.write( "3. a²-b² = ba-b²         3.multiplication postulate of equality.\r\n" );
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document.write( "3A. (a-b)(a+b) = b(a-b)  3A. Factoring both sides\r\n" );
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document.write( "3B. \"%28%28a%2Bb%29%28a-b%29%29%2F%28%28a-b%29%29\" = \"%28b%28a-b%29%29%2F%28a-b%29\"    3B. Division postulate\r\n" );
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document.write( "3C. \"%28%28a%2Bb%29%28cross%28a-b%29%29%29%2F%28%28cross%28a-b%29%29%29\" = \"%28b%28cross%28a-b%29%29%29%2F%28cross%28a-b%29%29\"  3C. Cancelling\r\n" );
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document.write( "4.  a+b = b              4.  What you get when you divide.   \r\n" );
document.write( "5.  b+b = b              5.  Substitution postulate using 1, a=b\r\n" );
document.write( "     2b = b              \r\n" );
document.write( "6.  \"2b%2Fb\" = \"b%2Fb\"               6. Division postulate of equality.\r\n" );
document.write( "7.   2 = 1               7.  Wow!!!\r\n" );
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document.write( "The fallacy is in 3B, the division postulate of equality states that\r\n" );
document.write( "\"If equal quantities are divided by equal nonzero quantities,\r\n" );
document.write( " the quotients are equal\".  The key word here is NONZERO.  We must always\r\n" );
document.write( "be sure that we are not dividing equal quantities by 0.  Here 0 is \r\n" );
document.write( "camouflaged as (a-b).  Step 1 stated that a=b, and that means that a-b=0.\r\n" );
document.write( "So when we divided by (a-b) in step 3B, we were dividing by zero, which is \r\n" );
document.write( "not defined in mathematics.\r\n" );
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document.write( "Edwin
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