document.write( "Question 1144645: y=1 if x is rational and y=0 if x irrational. how would you describe this on a graph. \n" ); document.write( "

Algebra.Com's Answer #765831 by ikleyn(52798) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "In a coordinate plane, draw two straight lines y= 0  and  y= 1.\r\n" );
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document.write( "Take a needle.   // If you don't know what a needle is, consult a dictionary.\r\n" );
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document.write( "Using the needle, make a hole in each point (x,1) on the line y= 1, where x is irrational.\r\n" );
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document.write( "In other words, using the needle, remove each point (x,1) on the line y= 1, where x is irrational.\r\n" );
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document.write( "    It is infinitely long job, if you do not use other special tools - but you are a patient person, isn't it :).\r\n" );
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document.write( "When you complete this job, you will get the requested graph.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is the description the problem asks for.\r
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\n" ); document.write( "\n" ); document.write( "Do not think that I am joking. I presented absolutely CLASSIC description to you.\r
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\n" ); document.write( "\n" ); document.write( "This function is called \"Dirichlet's function\", after great mathematician Peter Gustav Lejeune Dirichlet.\r
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\n" ); document.write( "\n" ); document.write( "For more information, see these links\r
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\n" ); document.write( "\n" ); document.write( "http://mathworld.wolfram.com/DirichletFunction.html\r
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\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Nowhere_continuous_function\r
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\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Peter_Gustav_Lejeune_Dirichlet\r
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